homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
equality (definitional, propositional, computational, judgemental, extensional, intensional, decidable)
identity type, equivalence of types, definitional isomorphism
isomorphism, weak equivalence, homotopy equivalence, weak homotopy equivalence, equivalence in an (∞,1)-category
Examples.
An equivalence of -groupoids is equivalently
an equivalence of (∞,1)-categories between (∞,1)-categories that happen to be ∞-groupoids,
In terms of presentation by topological spaces or simplicial sets (see at classical model structure on topological spaces and classical model structure on simplicial sets, respectively) this is:
If specifically presented by CW-complexes or Kan complexes, respectively, it is
Last revised on May 14, 2024 at 16:18:06. See the history of this page for a list of all contributions to it.