nLab stratified homotopy hypothesis

Contents

Context

Higher category theory

higher category theory

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 $(\infty, 1)$-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.