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363
Table of contents
363
1. Additive categories
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Category theory
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1.1. Abelian category
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Additive categories
1.2. Additive category
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Additive categories
1.3. Biproduct
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Additive categories
1.4. Double complex
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Additive categories
1.5. Exact category
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Additive categories
1.6. Exact functor
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Additive categories
1.7. Exact sequence
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Additive categories
1.8. Homotopy category of chain complexes
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Additive categories
1.9. Pre-abelian category
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Additive categories
1.10. Preadditive category
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Additive categories
1.11. Quasi-abelian category
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Additive categories
1.12. Semi-abelian category
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Additive categories
2. Categories in category theory
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Category theory
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2.1. Axiomatic foundations of topological spaces
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Categories in category theory
2.2. Category of abelian groups
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Categories in category theory
2.3. Category of groups
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Categories in category theory
2.4. Category of manifolds
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Categories in category theory
2.5. Category of medial magmas
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Categories in category theory
2.6. Category of metric spaces
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Categories in category theory
2.7. Category of preordered sets
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Categories in category theory
2.8. Category of rings
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Categories in category theory
2.9. Category of sets
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Categories in category theory
2.10. Category of small categories
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Categories in category theory
2.11. Category of topological spaces
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Categories in category theory
2.12. Category of topological vector spaces
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Categories in category theory
2.13. Comma category
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Categories in category theory
2.14. Connected category
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Categories in category theory
2.15. Derived category
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Categories in category theory
2.16. Differential graded category
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Categories in category theory
2.17. Discrete category
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Categories in category theory
2.18. FinSet
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Categories in category theory
2.19. Fukaya category
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Categories in category theory
2.20. Functor category
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Categories in category theory
2.21. Kleisli category
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Categories in category theory
2.22. Monoid (category theory)
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Categories in category theory
2.23. Regular category
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Categories in category theory
2.24. Small set (category theory)
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Categories in category theory
3. Category theorists
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Category theory
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3.1. André Joyal
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Category theorists
3.2. Andrée Ehresmann
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Category theorists
3.3. Charles Ehresmann
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Category theorists
3.4. Charles Rezk
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Category theorists
3.5. David Spivak
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Category theorists
3.6. Emily Riehl
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Category theorists
3.7. Eugenia Cheng
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Category theorists
3.8. Jacob Lurie
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Category theorists
3.9. Jacques Feldbau
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Category theorists
3.10. Jacques Riguet
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Category theorists
3.11. Jean Bénabou
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Category theorists
3.12. John C. Baez
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Category theorists
3.13. John C. Oxtoby
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Category theorists
3.14. John R. Isbell
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Category theorists
3.15. Kenneth Brown (mathematician)
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Category theorists
3.16. Martin Hyland
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Category theorists
3.17. Max Kelly
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Category theorists
3.18. Michael Barr (mathematician)
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Category theorists
3.19. Michael Shulman (mathematician)
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Category theorists
3.20. Myles Tierney
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Category theorists
3.21. Peter J. Freyd
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Category theorists
3.22. Peter Johnstone (mathematician)
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Category theorists
3.23. Richard J. Wood
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Category theorists
3.24. Ross Street
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Category theorists
3.25. Samuel Eilenberg
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Category theorists
3.26. Urs Schreiber
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Category theorists
3.27. Valeria de Paiva
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Category theorists
3.28. Věra Trnková
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Category theorists
3.29. William Lawvere
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Category theorists
4. Closed categories
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Category theory
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4.1. *-autonomous category
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Closed categories
4.2. Cartesian closed category
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Closed categories
4.3. Closed category
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Closed categories
4.4. Closed monoidal category
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Closed categories
4.5. Compact closed category
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Closed categories
5. Dagger categories
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Category theory
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5.1. Category of finite-dimensional Hilbert spaces
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Dagger categories
5.2. Dagger category
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Dagger categories
5.3. Dagger compact category
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Dagger categories
5.4. Dagger symmetric monoidal category
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Dagger categories
5.5. Ribbon category
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Dagger categories
6. Duality theories
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Category theory
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6.1. Adjoint functors
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Duality theories
6.2. Closure operators
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Duality theories
6.3. Self-duality
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Duality theories
6.4. Alvis–Curtis duality
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Duality theories
6.5. Artin–Verdier duality
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Duality theories
6.6. Born reciprocity
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Duality theories
6.7. Convex conjugate
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Duality theories
6.8. Dual abelian variety
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Duality theories
6.9. Dual polyhedron
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Duality theories
6.10. Dual system
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Duality theories
6.11. Dual wavelet
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Duality theories
6.12. Duality (electrical circuits)
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Duality theories
6.13. Duality (electricity and magnetism)
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Duality theories
6.14. Duality (mathematics)
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Duality theories
6.15. Duality (mechanical engineering)
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Duality theories
6.16. Duality (order theory)
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Duality theories
6.17. Duality (projective geometry)
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Duality theories
6.18. Esakia duality
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Duality theories
6.19. Fei–Ranis model of economic growth
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Duality theories
6.20. Grothendieck local duality
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Duality theories
6.21. Group scheme
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Duality theories
6.22. Hodge star operator
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Duality theories
6.23. Koszul duality
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Duality theories
6.24. Lefschetz duality
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Duality theories
6.25. List of dualities
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Duality theories
6.26. Local Tate duality
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Duality theories
6.27. Montonen–Olive duality
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Duality theories
6.28. Noncommutative harmonic analysis
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Duality theories
6.29. Pontryagin duality
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Duality theories
6.30. Reflexive space
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Duality theories
6.31. Riesz representation theorem
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Duality theories
6.32. Riesz–Markov–Kakutani representation theorem
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Duality theories
6.33. Seiberg duality
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Duality theories
6.34. Semi-reflexive space
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Duality theories
6.35. Six operations
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Duality theories
6.36. Stone duality
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Duality theories
6.37. Supporting functional
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Duality theories
6.38. Tannaka–Krein duality
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Duality theories
6.39. Tannakian formalism
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Duality theories
6.40. Tate duality
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Duality theories
6.41. Verdier duality
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Duality theories
7. Free algebraic structures
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Category theory
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7.1. Free Lie algebra
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Free algebraic structures
7.2. Free abelian group
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Free algebraic structures
7.3. Free algebra
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Free algebraic structures
7.4. Free category
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Free algebraic structures
7.5. Free group
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Free algebraic structures
7.6. Free independence
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Free algebraic structures
7.7. Term algebra
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Free algebraic structures
8. Functors
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Category theory
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8.1. Representable functors
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Functors
8.2. 2-functor
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Functors
8.3. Amnestic functor
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Functors
8.4. Derived functor
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Functors
8.5. Diagram (category theory)
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Functors
8.6. Dinatural transformation
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Functors
8.7. Dominant functor
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Functors
8.8. Effaceable functor
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Functors
8.9. End (category theory)
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Functors
8.10. Essentially surjective functor
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Functors
8.11. Final functor
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Functors
8.12. Forgetful functor
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Functors
8.13. Full and faithful functors
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Functors
8.14. Functor
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Functors
8.15. Hom functor
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Functors
8.16. Ind-completion
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Functors
8.17. Natural transformation
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Functors
8.18. Polynomial functor
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Functors
8.19. Presheaf (category theory)
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Functors
8.20. Profunctor
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Functors
8.21. Pseudo-functor
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Functors
8.22. Schur functor
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Functors
8.23. Smooth functor
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Functors
8.24. Span (category theory)
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Functors
8.25. Subfunctor
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Functors
8.26. Translation functor
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Functors
8.27. Zuckerman functor
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Functors
9. Higher category theory
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Category theory
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9.1. Bicategory
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Higher category theory
9.2. Conglomerate (mathematics)
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Higher category theory
9.3. Extranatural transformation
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Higher category theory
9.4. Higher Topos Theory
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Higher category theory
9.5. N-category number
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Higher category theory
9.6. N-monoid
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Higher category theory
9.7. Stable ∞-category
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Higher category theory
9.8. Strict 2-category
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Higher category theory
9.9. String diagram
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Higher category theory
9.10. Tetracategory
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Higher category theory
9.11. Tricategory
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Higher category theory
9.12. Weak n-category
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Higher category theory
9.13. ∞-topos
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Higher category theory
10. Limits (category theory)
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Category theory
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10.1. Coequalizer
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Limits (category theory)
10.2. Complete category
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Limits (category theory)
10.3. Coproduct
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Limits (category theory)
10.4. Equaliser (mathematics)
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Limits (category theory)
10.5. Initial and terminal objects
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Limits (category theory)
10.6. Limit (category theory)
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Limits (category theory)
10.7. Product (category theory)
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Limits (category theory)
10.8. Pullback (category theory)
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Limits (category theory)
10.9. Pushout (category theory)
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Limits (category theory)
11. Objects (category theory)
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Category theory
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11.1. Exponential object
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Objects (category theory)
11.2. Global element
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Objects (category theory)
11.3. Group object
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Objects (category theory)
11.4. List object
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Objects (category theory)
11.5. Projective object
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Objects (category theory)
11.6. Strict initial object
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Objects (category theory)
11.7. Subobject
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Objects (category theory)
11.8. Subobject classifier
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Objects (category theory)
12. Sheaf theory
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Category theory
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12.1. Geometry of divisors
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Sheaf theory
12.2. Algebraic analysis
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Sheaf theory
12.3. Base change theorems
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Sheaf theory
12.4. Constant sheaf
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Sheaf theory
12.5. Constructible sheaf
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Sheaf theory
12.6. Cousin problems
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Sheaf theory
12.7. D-module
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Sheaf theory
12.8. De Rham–Weil theorem
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Sheaf theory
12.9. Direct image functor
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Sheaf theory
12.10. Direct image with compact support
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Sheaf theory
12.11. Exceptional inverse image functor
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Sheaf theory
12.12. Exponential sheaf sequence
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Sheaf theory
12.13. Flat topology
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Sheaf theory
12.14. Gabriel–Rosenberg reconstruction theorem
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Sheaf theory
12.15. Gerbe
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Sheaf theory
12.16. Germ (mathematics)
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Sheaf theory
12.17. Grothendieck topology
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Sheaf theory
12.18. Hyperfunction
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Sheaf theory
12.19. Ideal sheaf
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Sheaf theory
12.20. Image functors for sheaves
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Sheaf theory
12.21. Injective sheaf
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Sheaf theory
12.22. Inverse image functor
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Sheaf theory
12.23. Invertible sheaf
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Sheaf theory
12.24. Leray's theorem
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Sheaf theory
12.25. Leray cover
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Sheaf theory
12.26. Leray spectral sequence
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Sheaf theory
12.27. Locally constant function
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Sheaf theory
12.28. Reflexive sheaf
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Sheaf theory
12.29. Restriction (mathematics)
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Sheaf theory
12.30. Ringed space
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Sheaf theory
12.31. Ringed topos
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Sheaf theory
12.32. Sheaf of algebras
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Sheaf theory
12.33. Sheaf of modules
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Sheaf theory
12.34. Sheaf on an algebraic stack
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Sheaf theory
12.35. Stalk (sheaf)
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Sheaf theory
12.36. Topos
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Sheaf theory
12.37. Torsion sheaf
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Sheaf theory
12.38. Étale topos
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Sheaf theory
13. AB5 category
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Category theory
14. Abstract nonsense
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Category theory
15. Accessible category
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Category theory
16. Adhesive category
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Category theory
17. Allegory (mathematics)
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Category theory
18. Anamorphism
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Category theory
19. Applied category theory
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Category theory
20. Beck's monadicity theorem
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Category theory
21. Brown's representability theorem
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Category theory
22. Bundle (mathematics)
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Category theory
23. Burnside category
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Category theory
24. Cartesian monoidal category
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Category theory
25. Categorical quantum mechanics
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Category theory
26. Categorical trace
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Category theory
27. Categories for the Working Mathematician
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Category theory
28. Category algebra
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Category theory
29. Category of representations
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Category theory
30. Center (category theory)
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Category theory
31. Chu space
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Category theory
32. Codensity monad
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Category theory
33. Coherence condition
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Category theory
34. Commutative diagram
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Category theory
35. Compact object (mathematics)
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Category theory
36. Concrete category
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Category theory
37. Cone (category theory)
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Category theory
38. Conservative functor
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Category theory
39. Corestriction
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Category theory
40. Cosmos (category theory)
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Category theory
41. Day convolution
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Category theory
42. Descent (mathematics)
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Category theory
43. Diagonal functor
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Category theory
44. Dialectica space
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Category theory
45. DisCoCat
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Category theory
46. Distributive category
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Category theory
47. Dual (category theory)
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Category theory
48. Duality theory for distributive lattices
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Category theory
49. Element (category theory)
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Category theory
50. Enriched category
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Category theory
51. Envelope (category theory)
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Category theory
52. Equivalence of categories
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Category theory
53. Essential monomorphism
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Category theory
54. Exact completion
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Category theory
55. Extensive category
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Category theory
56. F-algebra
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Category theory
57. F-coalgebra
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Category theory
58. Factorization system
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Category theory
59. Fiber functor
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Category theory
60. Fibred category
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Category theory
61. Filtered category
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Category theory
62. Finitely generated object
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Category theory
63. Freyd cover
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Category theory
64. Fusion category
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Category theory
65. Gamma-object
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Category theory
66. Generator (category theory)
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Category theory
67. Giraud subcategory
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Category theory
68. Globular set
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Category theory
69. Glossary of category theory
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Category theory
70. Graded category
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Category theory
71. Grothendieck's Galois theory
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Category theory
72. Grothendieck's relative point of view
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Category theory
73. Grothendieck category
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Category theory
74. Grothendieck construction
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Category theory
75. Grothendieck universe
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Category theory
76. Groupoid object
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Category theory
77. Hylomorphism (computer science)
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Category theory
78. Image (category theory)
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Category theory
79. Indexed category
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Category theory
80. Indiscrete category
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Category theory
81. Initial algebra
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Category theory
82. Injective cogenerator
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Category theory
83. Injective object
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Category theory
84. Inserter category
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Category theory
85. Internal category
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Category theory
86. Isbell conjugacy
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Category theory
87. Isomorphism-closed subcategory
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Category theory
88. Kan extension
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Category theory
89. Karoubi envelope
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Category theory
90. Kernel (category theory)
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Category theory
91. Krohn–Rhodes theory
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Category theory
92. Krull–Schmidt category
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Category theory
93. Lax functor
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Category theory
94. Lax natural transformation
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Category theory
95. Lift (mathematics)
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Category theory
96. Lifting property
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Category theory
97. Limit and colimit of presheaves
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Category theory
98. List of types of functions
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Category theory
99. Localization of a category
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Category theory
100. Localizing subcategory
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Category theory
101. Mac Lane coherence theorem
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Category theory
102. Monad (category theory)
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Category theory
103. Multicategory
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Category theory
104. Nerve (category theory)
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Category theory
105. Nodal decomposition
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Category theory
106. Opetope
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Category theory
107. Opposite category
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Category theory
108. Outline of category theory
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Category theory
109. Overcategory
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Category theory
110. Permutation category
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Category theory
111. Pointless topology
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Category theory
112. Polyad
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Category theory
113. Polygraph (mathematics)
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Category theory
114. Posetal category
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Category theory
115. Product category
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Category theory
116. Pseudo-abelian category
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Category theory
117. Pulation square
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Category theory
118. Q-category
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Category theory
119. Quantaloid
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Category theory
120. Quiver (mathematics)
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Category theory
121. Quotient category
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Category theory
122. Quotient of an abelian category
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Category theory
123. Refinement (category theory)
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Category theory
124. Section (category theory)
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Category theory
125. Segal category
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Category theory
126. Segal space
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Category theory
127. Semiautomaton
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Category theory
128. Sieve (category theory)
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Category theory
129. Simplicial localization
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Category theory
130. Simplicially enriched category
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Category theory
131. Skeleton (category theory)
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Category theory
132. Sketch (mathematics)
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Category theory
133. Spherical category
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Category theory
134. Stable model category
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Category theory
135. Stack (mathematics)
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Category theory
136. Subcategory
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Category theory
137. Subterminal object
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Category theory
138. Symplectic category
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Category theory
139. T-structure
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Category theory
140. Timeline of category theory and related mathematics
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Category theory
141. Topological category
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Category theory
142. Tower of objects
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Category theory
143. Universal property
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Category theory
144. Waldhausen category
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Category theory
145. Well-pointed category
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Category theory
1. Additive categories
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articles:
12
Category theory
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1.1. Abelian category
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Additive categories
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1.2. Additive category
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Additive categories
toc
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1.3. Biproduct
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Additive categories
toc
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1.4. Double complex
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Additive categories
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1.5. Exact category
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Additive categories
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1.6. Exact functor
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Additive categories
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1.7. Exact sequence
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Additive categories
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1.8. Homotopy category of chain complexes
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Additive categories
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1.9. Pre-abelian category
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Additive categories
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1.10. Preadditive category
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Additive categories
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1.11. Quasi-abelian category
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Additive categories
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1.12. Semi-abelian category
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Additive categories
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2. Categories in category theory
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articles:
24
Category theory
toc
wiki
2.1. Axiomatic foundations of topological spaces
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Categories in category theory
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wiki
2.2. Category of abelian groups
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Categories in category theory
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2.3. Category of groups
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Categories in category theory
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2.4. Category of manifolds
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Categories in category theory
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2.5. Category of medial magmas
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Categories in category theory
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2.6. Category of metric spaces
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Categories in category theory
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2.7. Category of preordered sets
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Categories in category theory
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2.8. Category of rings
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Categories in category theory
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2.9. Category of sets
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Categories in category theory
toc
wiki
2.10. Category of small categories
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Categories in category theory
toc
wiki
2.11. Category of topological spaces
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Categories in category theory
toc
wiki
2.12. Category of topological vector spaces
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Categories in category theory
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wiki
2.13. Comma category
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Categories in category theory
toc
wiki
2.14. Connected category
split
Categories in category theory
toc
wiki
2.15. Derived category
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Categories in category theory
toc
wiki
2.16. Differential graded category
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Categories in category theory
toc
wiki
2.17. Discrete category
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Categories in category theory
toc
wiki
2.18. FinSet
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Categories in category theory
toc
wiki
2.19. Fukaya category
split
Categories in category theory
toc
wiki
2.20. Functor category
split
Categories in category theory
toc
wiki
2.21. Kleisli category
split
Categories in category theory
toc
wiki
2.22. Monoid (category theory)
split
Categories in category theory
toc
wiki
2.23. Regular category
split
Categories in category theory
toc
wiki
2.24. Small set (category theory)
split
Categories in category theory
toc
wiki
3. Category theorists
split
articles:
29
Category theory
toc
wiki
3.1. André Joyal
split
Category theorists
toc
wiki
3.2. Andrée Ehresmann
split
Category theorists
toc
wiki
3.3. Charles Ehresmann
split
Category theorists
toc
wiki
3.4. Charles Rezk
split
Category theorists
toc
wiki
3.5. David Spivak
split
Category theorists
toc
wiki
3.6. Emily Riehl
split
Category theorists
toc
wiki
3.7. Eugenia Cheng
split
Category theorists
toc
wiki
3.8. Jacob Lurie
split
Category theorists
toc
wiki
3.9. Jacques Feldbau
split
Category theorists
toc
wiki
3.10. Jacques Riguet
split
Category theorists
toc
wiki
3.11. Jean Bénabou
split
Category theorists
toc
wiki
3.12. John C. Baez
split
Category theorists
toc
wiki
3.13. John C. Oxtoby
split
Category theorists
toc
wiki
3.14. John R. Isbell
split
Category theorists
toc
wiki
3.15. Kenneth Brown (mathematician)
split
Category theorists
toc
wiki
3.16. Martin Hyland
split
Category theorists
toc
wiki
3.17. Max Kelly
split
Category theorists
toc
wiki
3.18. Michael Barr (mathematician)
split
Category theorists
toc
wiki
3.19. Michael Shulman (mathematician)
split
Category theorists
toc
wiki
3.20. Myles Tierney
split
Category theorists
toc
wiki
3.21. Peter J. Freyd
split
Category theorists
toc
wiki
3.22. Peter Johnstone (mathematician)
split
Category theorists
toc
wiki
3.23. Richard J. Wood
split
Category theorists
toc
wiki
3.24. Ross Street
split
Category theorists
toc
wiki
3.25. Samuel Eilenberg
split
Category theorists
toc
wiki
3.26. Urs Schreiber
split
Category theorists
toc
wiki
3.27. Valeria de Paiva
split
Category theorists
toc
wiki
3.28. Věra Trnková
split
Category theorists
toc
wiki
3.29. William Lawvere
split
Category theorists
toc
wiki
4. Closed categories
split
articles:
5
Category theory
toc
wiki
4.1. *-autonomous category
split
Closed categories
toc
wiki
4.2. Cartesian closed category
split
Closed categories
toc
wiki
4.3. Closed category
split
Closed categories
toc
wiki
4.4. Closed monoidal category
split
Closed categories
toc
wiki
4.5. Compact closed category
split
Closed categories
toc
wiki
5. Dagger categories
split
articles:
5
Category theory
toc
wiki
5.1. Category of finite-dimensional Hilbert spaces
split
Dagger categories
toc
wiki
5.2. Dagger category
split
Dagger categories
toc
wiki
5.3. Dagger compact category
split
Dagger categories
toc
wiki
5.4. Dagger symmetric monoidal category
split
Dagger categories
toc
wiki
5.5. Ribbon category
split
Dagger categories
toc
wiki
6. Duality theories
split
articles:
41
Category theory
toc
wiki
6.1. Adjoint functors
split
Duality theories
toc
wiki
6.2. Closure operators
split
Duality theories
toc
wiki
6.3. Self-duality
split
Duality theories
toc
wiki
6.4. Alvis–Curtis duality
split
Duality theories
toc
wiki
6.5. Artin–Verdier duality
split
Duality theories
toc
wiki
6.6. Born reciprocity
split
Duality theories
toc
wiki
6.7. Convex conjugate
split
Duality theories
toc
wiki
6.8. Dual abelian variety
split
Duality theories
toc
wiki
6.9. Dual polyhedron
split
Duality theories
toc
wiki
6.10. Dual system
split
Duality theories
toc
wiki
6.11. Dual wavelet
split
Duality theories
toc
wiki
6.12. Duality (electrical circuits)
split
Duality theories
toc
wiki
6.13. Duality (electricity and magnetism)
split
Duality theories
toc
wiki
6.14. Duality (mathematics)
split
Duality theories
toc
wiki
6.15. Duality (mechanical engineering)
split
Duality theories
toc
wiki
6.16. Duality (order theory)
split
Duality theories
toc
wiki
6.17. Duality (projective geometry)
split
Duality theories
toc
wiki
6.18. Esakia duality
split
Duality theories
toc
wiki
6.19. Fei–Ranis model of economic growth
split
Duality theories
toc
wiki
6.20. Grothendieck local duality
split
Duality theories
toc
wiki
6.21. Group scheme
split
Duality theories
toc
wiki
6.22. Hodge star operator
split
Duality theories
toc
wiki
6.23. Koszul duality
split
Duality theories
toc
wiki
6.24. Lefschetz duality
split
Duality theories
toc
wiki
6.25. List of dualities
split
Duality theories
toc
wiki
6.26. Local Tate duality
split
Duality theories
toc
wiki
6.27. Montonen–Olive duality
split
Duality theories
toc
wiki
6.28. Noncommutative harmonic analysis
split
Duality theories
toc
wiki
6.29. Pontryagin duality
split
Duality theories
toc
wiki
6.30. Reflexive space
split
Duality theories
toc
wiki
6.31. Riesz representation theorem
split
Duality theories
toc
wiki
6.32. Riesz–Markov–Kakutani representation theorem
split
Duality theories
toc
wiki
6.33. Seiberg duality
split
Duality theories
toc
wiki
6.34. Semi-reflexive space
split
Duality theories
toc
wiki
6.35. Six operations
split
Duality theories
toc
wiki
6.36. Stone duality
split
Duality theories
toc
wiki
6.37. Supporting functional
split
Duality theories
toc
wiki
6.38. Tannaka–Krein duality
split
Duality theories
toc
wiki
6.39. Tannakian formalism
split
Duality theories
toc
wiki
6.40. Tate duality
split
Duality theories
toc
wiki
6.41. Verdier duality
split
Duality theories
toc
wiki
7. Free algebraic structures
split
articles:
7
Category theory
toc
wiki
7.1. Free Lie algebra
split
Free algebraic structures
toc
wiki
7.2. Free abelian group
split
Free algebraic structures
toc
wiki
7.3. Free algebra
split
Free algebraic structures
toc
wiki
7.4. Free category
split
Free algebraic structures
toc
wiki
7.5. Free group
split
Free algebraic structures
toc
wiki
7.6. Free independence
split
Free algebraic structures
toc
wiki
7.7. Term algebra
split
Free algebraic structures
toc
wiki
8. Functors
split
articles:
27
Category theory
toc
wiki
8.1. Representable functors
split
Functors
toc
wiki
8.2. 2-functor
split
Functors
toc
wiki
8.3. Amnestic functor
split
Functors
toc
wiki
8.4. Derived functor
split
Functors
toc
wiki
8.5. Diagram (category theory)
split
Functors
toc
wiki
8.6. Dinatural transformation
split
Functors
toc
wiki
8.7. Dominant functor
split
Functors
toc
wiki
8.8. Effaceable functor
split
Functors
toc
wiki
8.9. End (category theory)
split
Functors
toc
wiki
8.10. Essentially surjective functor
split
Functors
toc
wiki
8.11. Final functor
split
Functors
toc
wiki
8.12. Forgetful functor
split
Functors
toc
wiki
8.13. Full and faithful functors
split
Functors
toc
wiki
8.14. Functor
split
Functors
toc
wiki
8.15. Hom functor
split
Functors
toc
wiki
8.16. Ind-completion
split
Functors
toc
wiki
8.17. Natural transformation
split
Functors
toc
wiki
8.18. Polynomial functor
split
Functors
toc
wiki
8.19. Presheaf (category theory)
split
Functors
toc
wiki
8.20. Profunctor
split
Functors
toc
wiki
8.21. Pseudo-functor
split
Functors
toc
wiki
8.22. Schur functor
split
Functors
toc
wiki
8.23. Smooth functor
split
Functors
toc
wiki
8.24. Span (category theory)
split
Functors
toc
wiki
8.25. Subfunctor
split
Functors
toc
wiki
8.26. Translation functor
split
Functors
toc
wiki
8.27. Zuckerman functor
split
Functors
toc
wiki
9. Higher category theory
split
articles:
13
Category theory
toc
wiki
9.1. Bicategory
split
Higher category theory
toc
wiki
9.2. Conglomerate (mathematics)
split
Higher category theory
toc
wiki
9.3. Extranatural transformation
split
Higher category theory
toc
wiki
9.4. Higher Topos Theory
split
Higher category theory
toc
wiki
9.5. N-category number
split
Higher category theory
toc
wiki
9.6. N-monoid
split
Higher category theory
toc
wiki
9.7. Stable ∞-category
split
Higher category theory
toc
wiki
9.8. Strict 2-category
split
Higher category theory
toc
wiki
9.9. String diagram
split
Higher category theory
toc
wiki
9.10. Tetracategory
split
Higher category theory
toc
wiki
9.11. Tricategory
split
Higher category theory
toc
wiki
9.12. Weak n-category
split
Higher category theory
toc
wiki
9.13. ∞-topos
split
Higher category theory
toc
wiki
10. Limits (category theory)
split
articles:
9
Category theory
toc
wiki
10.1. Coequalizer
split
Limits (category theory)
toc
wiki
10.2. Complete category
split
Limits (category theory)
toc
wiki
10.3. Coproduct
split
Limits (category theory)
toc
wiki
10.4. Equaliser (mathematics)
split
Limits (category theory)
toc
wiki
10.5. Initial and terminal objects
split
Limits (category theory)
toc
wiki
10.6. Limit (category theory)
split
Limits (category theory)
toc
wiki
10.7. Product (category theory)
split
Limits (category theory)
toc
wiki
10.8. Pullback (category theory)
split
Limits (category theory)
toc
wiki
10.9. Pushout (category theory)
split
Limits (category theory)
toc
wiki
11. Objects (category theory)
split
articles:
8
Category theory
toc
wiki
11.1. Exponential object
split
Objects (category theory)
toc
wiki
11.2. Global element
split
Objects (category theory)
toc
wiki
11.3. Group object
split
Objects (category theory)
toc
wiki
11.4. List object
split
Objects (category theory)
toc
wiki
11.5. Projective object
split
Objects (category theory)
toc
wiki
11.6. Strict initial object
split
Objects (category theory)
toc
wiki
11.7. Subobject
split
Objects (category theory)
toc
wiki
11.8. Subobject classifier
split
Objects (category theory)
toc
wiki
12. Sheaf theory
split
articles:
38
Category theory
toc
wiki
12.1. Geometry of divisors
split
Sheaf theory
toc
wiki
12.2. Algebraic analysis
split
Sheaf theory
toc
wiki
12.3. Base change theorems
split
Sheaf theory
toc
wiki
12.4. Constant sheaf
split
Sheaf theory
toc
wiki
12.5. Constructible sheaf
split
Sheaf theory
toc
wiki
12.6. Cousin problems
split
Sheaf theory
toc
wiki
12.7. D-module
split
Sheaf theory
toc
wiki
12.8. De Rham–Weil theorem
split
Sheaf theory
toc
wiki
12.9. Direct image functor
split
Sheaf theory
toc
wiki
12.10. Direct image with compact support
split
Sheaf theory
toc
wiki
12.11. Exceptional inverse image functor
split
Sheaf theory
toc
wiki
12.12. Exponential sheaf sequence
split
Sheaf theory
toc
wiki
12.13. Flat topology
split
Sheaf theory
toc
wiki
12.14. Gabriel–Rosenberg reconstruction theorem
split
Sheaf theory
toc
wiki
12.15. Gerbe
split
Sheaf theory
toc
wiki
12.16. Germ (mathematics)
split
Sheaf theory
toc
wiki
12.17. Grothendieck topology
split
Sheaf theory
toc
wiki
12.18. Hyperfunction
split
Sheaf theory
toc
wiki
12.19. Ideal sheaf
split
Sheaf theory
toc
wiki
12.20. Image functors for sheaves
split
Sheaf theory
toc
wiki
12.21. Injective sheaf
split
Sheaf theory
toc
wiki
12.22. Inverse image functor
split
Sheaf theory
toc
wiki
12.23. Invertible sheaf
split
Sheaf theory
toc
wiki
12.24. Leray's theorem
split
Sheaf theory
toc
wiki
12.25. Leray cover
split
Sheaf theory
toc
wiki
12.26. Leray spectral sequence
split
Sheaf theory
toc
wiki
12.27. Locally constant function
split
Sheaf theory
toc
wiki
12.28. Reflexive sheaf
split
Sheaf theory
toc
wiki
12.29. Restriction (mathematics)
split
Sheaf theory
toc
wiki
12.30. Ringed space
split
Sheaf theory
toc
wiki
12.31. Ringed topos
split
Sheaf theory
toc
wiki
12.32. Sheaf of algebras
split
Sheaf theory
toc
wiki
12.33. Sheaf of modules
split
Sheaf theory
toc
wiki
12.34. Sheaf on an algebraic stack
split
Sheaf theory
toc
wiki
12.35. Stalk (sheaf)
split
Sheaf theory
toc
wiki
12.36. Topos
split
Sheaf theory
toc
wiki
12.37. Torsion sheaf
split
Sheaf theory
toc
wiki
12.38. Étale topos
split
Sheaf theory
toc
wiki
13. AB5 category
split
Category theory
toc
wiki
14. Abstract nonsense
split
Category theory
toc
wiki
15. Accessible category
split
Category theory
toc
wiki
16. Adhesive category
split
Category theory
toc
wiki
17. Allegory (mathematics)
split
Category theory
toc
wiki
18. Anamorphism
split
Category theory
toc
wiki
19. Applied category theory
split
Category theory
toc
wiki
20. Beck's monadicity theorem
split
Category theory
toc
wiki
21. Brown's representability theorem
split
Category theory
toc
wiki
22. Bundle (mathematics)
split
Category theory
toc
wiki
23. Burnside category
split
Category theory
toc
wiki
24. Cartesian monoidal category
split
Category theory
toc
wiki
25. Categorical quantum mechanics
split
Category theory
toc
wiki
26. Categorical trace
split
Category theory
toc
wiki
27. Categories for the Working Mathematician
split
Category theory
toc
wiki
28. Category algebra
split
Category theory
toc
wiki
29. Category of representations
split
Category theory
toc
wiki
30. Center (category theory)
split
Category theory
toc
wiki
31. Chu space
split
Category theory
toc
wiki
32. Codensity monad
split
Category theory
toc
wiki
33. Coherence condition
split
Category theory
toc
wiki
34. Commutative diagram
split
Category theory
toc
wiki
35. Compact object (mathematics)
split
Category theory
toc
wiki
36. Concrete category
split
Category theory
toc
wiki
37. Cone (category theory)
split
Category theory
toc
wiki
38. Conservative functor
split
Category theory
toc
wiki
39. Corestriction
split
Category theory
toc
wiki
40. Cosmos (category theory)
split
Category theory
toc
wiki
41. Day convolution
split
Category theory
toc
wiki
42. Descent (mathematics)
split
Category theory
toc
wiki
43. Diagonal functor
split
Category theory
toc
wiki
44. Dialectica space
split
Category theory
toc
wiki
45. DisCoCat
split
Category theory
toc
wiki
46. Distributive category
split
Category theory
toc
wiki
47. Dual (category theory)
split
Category theory
toc
wiki
48. Duality theory for distributive lattices
split
Category theory
toc
wiki
49. Element (category theory)
split
Category theory
toc
wiki
50. Enriched category
split
Category theory
toc
wiki
51. Envelope (category theory)
split
Category theory
toc
wiki
52. Equivalence of categories
split
Category theory
toc
wiki
53. Essential monomorphism
split
Category theory
toc
wiki
54. Exact completion
split
Category theory
toc
wiki
55. Extensive category
split
Category theory
toc
wiki
56. F-algebra
split
Category theory
toc
wiki
57. F-coalgebra
split
Category theory
toc
wiki
58. Factorization system
split
Category theory
toc
wiki
59. Fiber functor
split
Category theory
toc
wiki
60. Fibred category
split
Category theory
toc
wiki
61. Filtered category
split
Category theory
toc
wiki
62. Finitely generated object
split
Category theory
toc
wiki
63. Freyd cover
split
Category theory
toc
wiki
64. Fusion category
split
Category theory
toc
wiki
65. Gamma-object
split
Category theory
toc
wiki
66. Generator (category theory)
split
Category theory
toc
wiki
67. Giraud subcategory
split
Category theory
toc
wiki
68. Globular set
split
Category theory
toc
wiki
69. Glossary of category theory
split
Category theory
toc
wiki
70. Graded category
split
Category theory
toc
wiki
71. Grothendieck's Galois theory
split
Category theory
toc
wiki
72. Grothendieck's relative point of view
split
Category theory
toc
wiki
73. Grothendieck category
split
Category theory
toc
wiki
74. Grothendieck construction
split
Category theory
toc
wiki
75. Grothendieck universe
split
Category theory
toc
wiki
76. Groupoid object
split
Category theory
toc
wiki
77. Hylomorphism (computer science)
split
Category theory
toc
wiki
78. Image (category theory)
split
Category theory
toc
wiki
79. Indexed category
split
Category theory
toc
wiki
80. Indiscrete category
split
Category theory
toc
wiki
81. Initial algebra
split
Category theory
toc
wiki
82. Injective cogenerator
split
Category theory
toc
wiki
83. Injective object
split
Category theory
toc
wiki
84. Inserter category
split
Category theory
toc
wiki
85. Internal category
split
Category theory
toc
wiki
86. Isbell conjugacy
split
Category theory
toc
wiki
87. Isomorphism-closed subcategory
split
Category theory
toc
wiki
88. Kan extension
split
Category theory
toc
wiki
89. Karoubi envelope
split
Category theory
toc
wiki
90. Kernel (category theory)
split
Category theory
toc
wiki
91. Krohn–Rhodes theory
split
Category theory
toc
wiki
92. Krull–Schmidt category
split
Category theory
toc
wiki
93. Lax functor
split
Category theory
toc
wiki
94. Lax natural transformation
split
Category theory
toc
wiki
95. Lift (mathematics)
split
Category theory
toc
wiki
96. Lifting property
split
Category theory
toc
wiki
97. Limit and colimit of presheaves
split
Category theory
toc
wiki
98. List of types of functions
split
Category theory
toc
wiki
99. Localization of a category
split
Category theory
toc
wiki
100. Localizing subcategory
split
Category theory
toc
wiki
101. Mac Lane coherence theorem
split
Category theory
toc
wiki
102. Monad (category theory)
split
Category theory
toc
wiki
103. Multicategory
split
Category theory
toc
wiki
104. Nerve (category theory)
split
Category theory
toc
wiki
105. Nodal decomposition
split
Category theory
toc
wiki
106. Opetope
split
Category theory
toc
wiki
107. Opposite category
split
Category theory
toc
wiki
108. Outline of category theory
split
Category theory
toc
wiki
109. Overcategory
split
Category theory
toc
wiki
110. Permutation category
split
Category theory
toc
wiki
111. Pointless topology
split
Category theory
toc
wiki
112. Polyad
split
Category theory
toc
wiki
113. Polygraph (mathematics)
split
Category theory
toc
wiki
114. Posetal category
split
Category theory
toc
wiki
115. Product category
split
Category theory
toc
wiki
116. Pseudo-abelian category
split
Category theory
toc
wiki
117. Pulation square
split
Category theory
toc
wiki
118. Q-category
split
Category theory
toc
wiki
119. Quantaloid
split
Category theory
toc
wiki
120. Quiver (mathematics)
split
Category theory
toc
wiki
121. Quotient category
split
Category theory
toc
wiki
122. Quotient of an abelian category
split
Category theory
toc
wiki
123. Refinement (category theory)
split
Category theory
toc
wiki
124. Section (category theory)
split
Category theory
toc
wiki
125. Segal category
split
Category theory
toc
wiki
126. Segal space
split
Category theory
toc
wiki
127. Semiautomaton
split
Category theory
toc
wiki
128. Sieve (category theory)
split
Category theory
toc
wiki
129. Simplicial localization
split
Category theory
toc
wiki
130. Simplicially enriched category
split
Category theory
toc
wiki
131. Skeleton (category theory)
split
Category theory
toc
wiki
132. Sketch (mathematics)
split
Category theory
toc
wiki
133. Spherical category
split
Category theory
toc
wiki
134. Stable model category
split
Category theory
toc
wiki
135. Stack (mathematics)
split
Category theory
toc
wiki
136. Subcategory
split
Category theory
toc
wiki
137. Subterminal object
split
Category theory
toc
wiki
138. Symplectic category
split
Category theory
toc
wiki
139. T-structure
split
Category theory
toc
wiki
140. Timeline of category theory and related mathematics
split
Category theory
toc
wiki
141. Topological category
split
Category theory
toc
wiki
142. Tower of objects
split
Category theory
toc
wiki
143. Universal property
split
Category theory
toc
wiki
144. Waldhausen category
split
Category theory
toc
wiki
145. Well-pointed category
split
Category theory
toc
wiki
Ancestors
Fields of abstract algebra
Fields of mathematics
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