@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",

}

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 -