Homotopy (Co)limits via Homotopy (Co)ends in General Combinatorial Model Categories

Sergey Arkhipov; Sebastian Ørsted

doi:10.1007/s10485-023-09747-8

Homotopy (Co)limits via Homotopy (Co)ends in General Combinatorial Model Categories

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

2 Citationer (Scopus)

Abstract

We prove and explain several classical formulae for homotopy (co)limits in general (combinatorial) model categories which are not necessarily simplicially enriched. Importantly, we prove versions of the Bousfield–Kan formula and the fat totalization formula in this complete generality. We finish with a proof that homotopy-final functors preserve homotopy limits, again in complete generality.

Originalsprog	Engelsk
Artikelnummer	47
Tidsskrift	Applied Categorical Structures
Vol/bind	31
Nummer	6
ISSN	0927-2852
DOI	https://doi.org/10.1007/s10485-023-09747-8
Status	Udgivet - nov. 2023

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abstract = "We prove and explain several classical formulae for homotopy (co)limits in general (combinatorial) model categories which are not necessarily simplicially enriched. Importantly, we prove versions of the Bousfield–Kan formula and the fat totalization formula in this complete generality. We finish with a proof that homotopy-final functors preserve homotopy limits, again in complete generality.",

keywords = "Bousfield–Kan formula, Category theory, Derived functors, Homotopy limit, Model categories, Simplicial sets",

author = "Sergey Arkhipov and Sebastian {\O}rsted",

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AU - Ørsted, Sebastian

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AB - We prove and explain several classical formulae for homotopy (co)limits in general (combinatorial) model categories which are not necessarily simplicially enriched. Importantly, we prove versions of the Bousfield–Kan formula and the fat totalization formula in this complete generality. We finish with a proof that homotopy-final functors preserve homotopy limits, again in complete generality.

KW - Bousfield–Kan formula

KW - Category theory

KW - Derived functors

KW - Homotopy limit

KW - Model categories

KW - Simplicial sets

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Homotopy (Co)limits via Homotopy (Co)ends in General Combinatorial Model Categories

Abstract

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