A stratified Kan-Quillen equivalence

TL;DR

This paper establishes a Quillen equivalence between two model categories representing stratified spaces and introduces vertical filtered CW-complexes as a new, effective model for their homotopy theory.

Contribution

It demonstrates a Quillen equivalence between filtered simplicial sets and filtered spaces, and introduces vertical filtered CW-complexes as a novel model for stratified spaces.

Findings

Quillen equivalence between filtered simplicial sets and filtered spaces

Introduction of vertical filtered CW-complexes as a new model

Enhanced understanding of the homotopy theory of stratified spaces

Abstract

We exhibit a Quillen equivalence between two model categories encoding the homotopy theory of stratified spaces : the model category of filtered simplicial sets, and that of filtered spaces. Additionally, we introduce a new class of filtered spaces, that of vertical filtered CW-complexes, providing a nice model for the homotopy category of stratified spaces.