2021/02/09 by Sylvain Douteau, Douteau, Sylvain
Mathematics · #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2102.04876
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.