3 citations · 3 across the 4 of their papers we have counts for
5 papers
Old and new structures on Ran spaces: Length structures, completeness, and conicality
Sylvain Douteau, Marie Labeye
We study topologies on Ran spaces. In the literature, two distinct topologies frequently appear: the Hausdorff topology, and a finer one constructed as a colimit, that we call the…
From homotopy links to stratified homotopy theories
Sylvain Douteau, Lukas Waas
In previous work, the first author defined homotopy theories for stratified spaces from a simplicial and a topological perspective. In both frameworks stratified weak-equivalences…
A stratified Kan-Quillen equivalence
Sylvain Douteau
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 filter…
Stratified Homotopy Theory
Sylvain Douteau
A stratified space is a topological space together with a decomposition into strata corresponding to different types of singularities. Examples of such spaces appear everywhere in…
A Simplicial Approach to Stratified Homotopy Theory
Sylvain Douteau
In this article we consider the homotopy theory of stratified spaces through a simplicial point of view. We first consider a model category of filtered simplicial sets over some fi…