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The homotopy category is a fundamental concept in algebraic topology and homotopy theory that captures the idea of "homotopy equivalence" between topological spaces (or more generally, between objects in a category) in a categorical framework. To understand the homotopy category, we begin with the following components: 1. **Topological Spaces and Continuous Maps**: In topology, we often deal with spaces that can be continuously deformed into each other.

Ancestors (6)

  1. Homotopy theory
  2. Algebraic topology
  3. Fields of abstract algebra
  4. Fields of mathematics
  5. Mathematics
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