New York Journal of Mathematics
Volume 25 (2019), 1485-1510


Philippe Gaucher

Enriched diagrams of topological spaces over locally contractible enriched categories

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Published: December 18, 2019.
Keywords: d-space, topologically enriched diagram, combinatorial model category, accessible model category, homotopy colimit, locally presentable category, topologically enriched category, projective model structure, injective model structure.
Subject: 18C35,55U35,18G55,68Q85.

It is proved that the projective model structure of the category of topologically enriched diagrams of topological spaces over a locally contractible topologically enriched small category is Quillen equivalent to the standard Quillen model structure of topological spaces. We give a geometric interpretation of this fact in directed homotopy.


I thank Tim Campion for Theorem 3.2 and Tyler Lawson for Theorem 8.1. I also thank Asaf Karagila for [21] even if his contribution is not necessary anymore in this new version (it suffices in the proof of Theorem 3.2 to choose a regular cardinal μ > λ such that μ ⊳ λ instead of μλ = μ) and Tim Porter for valuable email discussions. I thank the anonymous referee for the detailed report.

Author information

Philippe Gaucher:
Université de Paris
F-75013 Paris, France