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
A functor on spaces (e.g. some cohomology functor) is called “homotopy invariant” if it does not distinguish between a space and the space , where is an interval; equivalently if it takes the same value on morphisms which are related by a (left) homotopy.
The term homotopy invariant may also refer to the refinement of invariants to homotopy theory, hence to homotopy fixed points.
A generalized (Eilenberg-Steenrod) cohomology-functor is by definition homotopy invariant, but for instance its refinement to differential cohomology in general no longer is.
representation theory and equivariant cohomology in terms of (∞,1)-topos theory/homotopy type theory (FSS 12 I, exmp. 4.4):
Last revised on April 20, 2017 at 14:27:27. See the history of this page for a list of all contributions to it.