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363
Table of contents
363
1. Additive categories
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Category theory
12
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
29
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
5
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
Ancestors
Fields of abstract algebra
Fields of mathematics
Mathematics
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