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arXiv · 1911.04921

Homotopy theory of stratified spaces

Sylvain Douteau
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Abstract

In this article, we construct a cofibrantly generated model structure on the category of spaces stratified over a fixed poset, and show that it is Quillen-equivalent to a category of diagrams of simplicial sets. Then, considering all those model structures together, we construct a cofibrantly generated model structure on the category of all stratified spaces. In both model categories, weak-equivalences are characterized by stratified homotopy groups.

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Sylvain Douteau. 2020-05-26. Homotopy theory of stratified spaces. https://doi.org/10.2140/agt.2021.21.507

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