Dwyer-Kan Equivalences Induce Equivalences on Topologically Enriched Presheaves
Alexander K\"orschgen
TL;DR
This paper discusses how Dwyer-Kan equivalences between small topological categories lead to Quillen equivalences in their associated topologically enriched presheaf categories, providing a detailed proof of this result.
Contribution
It offers a detailed account and proof of how Dwyer-Kan equivalences induce Quillen equivalences on topologically enriched presheaves.
Findings
Dwyer-Kan equivalences induce Quillen equivalences
Detailed proof provided for the main result
Clarifies the relationship between topological categories and presheaf categories
Abstract
This brief note elaborates on a result by Gepner and Henriques. They have shown that a Dwyer-Kan equivalence between two small, topological categories gives rise to a Quillen equivalence of the associated categories of topologically enriched presheaves. We present a more detailed account of their proof.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra