nLab
stratified homotopy hypothesis

Contents

Context

Homotopy theory

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

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

Idea

Where the homotopy hypothesis is the assertion that ∞-groupoids are equivalent to topological spaces (considered modulo weak homotopy equivalence), in AFR15 the authors construct an equivalence for (∞,1)-categories. They do so in terms of what are called striation sheaves, which are sheaves on conically smooth stratified spaces satisfying a certain descent condition.

The construction relies on a fully faithful embedding of conically smooth stratified spaces, and conically smooth maps among them, into (,1)(\infty, 1)-categories via the exit-path functor, which maps stratified spaces to paths within them that once they leave a stratum do not re-enter it.

References

Created on October 27, 2017 at 05:44:51. See the history of this page for a list of all contributions to it.