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math.AT2026
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…
math.AT2021
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…
math.AT2019
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…