 

Philippe Gaucher
Enriched diagrams of topological spaces over locally contractible enriched categories
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print


Published: 
December 18, 2019. 
Keywords: 
dspace, 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. 


Abstract
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. 

Acknowledgements
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
μ^{λ} = μ) and Tim Porter for valuable email discussions. I thank the anonymous referee for the detailed report.


Author information
Philippe Gaucher:
Université de Paris
IRIF, CNRS
F75013 Paris, France
http://www.irif.fr/~gaucher

