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Sergey Arkhipov

Homotopy (co)limits via homotopy (co)ends in general combinatorial model categories

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Homotopy (co)limits via homotopy (co)ends in general combinatorial model categories. / Arkhipov, Sergey; Ørsted, Sebastian.

2018.

Research output: Working paper/Preprint Working paperResearchpeer-review

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@techreport{541d969f8fda4fd2aad2dd27c8eee3af,
title = "Homotopy (co)limits via homotopy (co)ends in general combinatorial model categories",
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 = "math.CT, 18G55, 18D99, 55U35, 18G30",
author = "Sergey Arkhipov and Sebastian {\O}rsted",
note = "13 pages; updated the abstract and introduction",
year = "2018",
month = jul,
day = "9",
language = "English",
series = "arXiv",
type = "WorkingPaper",

}

RIS

TY - UNPB

T1 - Homotopy (co)limits via homotopy (co)ends in general combinatorial model categories

AU - Arkhipov, Sergey

AU - Ørsted, Sebastian

N1 - 13 pages; updated the abstract and introduction

PY - 2018/7/9

Y1 - 2018/7/9

N2 - 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.

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 - math.CT

KW - 18G55, 18D99, 55U35, 18G30

M3 - Working paper

T3 - arXiv

BT - Homotopy (co)limits via homotopy (co)ends in general combinatorial model categories

ER -