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
Methods from abstract homotopy theory can be used to define a suitable notion of homotopy equivalence for inverse semigroups. As an application of this theory, one can prove a theorem for inverse semigroup homomorphisms which is the exact counterpart of the well-known result in topology which states that every continuous function can be factorised into a homotopy equivalence followed by a fibration.
In the paper LMP it is shown that this factorisation is isomorphic to the one constructed by Steinberg in his Fibration Theorem, originally proved using a generalisation of Tilson’s derived category.
Last revised on December 1, 2015 at 07:25:19. See the history of this page for a list of all contributions to it.