Coalgebraic models for combinatorial model categories

Michael Ching; Emily Riehl

doi:10.4310/HHA.2014.v16.n2.a9

Coalgebraic models for combinatorial model categories

Michael Ching, Emily Riehl

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

We show that the category of algebraically cofibrant objects in a combinatorial and simplicial model category A has a model structure that is left-induced from that on A. In particular, it follows that any presentable model category is Quillen equivalent (via a single Quillen equivalence) to one in which all objects are cofibrant.

Original language	English
Pages (from-to)	171-184
Number of pages	14
Journal	Homology, Homotopy and Applications
Volume	16
Issue number	2
DOIs	https://doi.org/10.4310/HHA.2014.v16.n2.a9
Publication status	Published - 2014
Externally published	Yes

Keywords

Coalgebra
Cofibrant object
Model category

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10.4310/HHA.2014.v16.n2.a9

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title = "Coalgebraic models for combinatorial model categories",

abstract = "We show that the category of algebraically cofibrant objects in a combinatorial and simplicial model category A has a model structure that is left-induced from that on A. In particular, it follows that any presentable model category is Quillen equivalent (via a single Quillen equivalence) to one in which all objects are cofibrant.",

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author = "Michael Ching and Emily Riehl",

year = "2014",

doi = "10.4310/HHA.2014.v16.n2.a9",

language = "English",

volume = "16",

pages = "171--184",

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T1 - Coalgebraic models for combinatorial model categories

AU - Ching, Michael

AU - Riehl, Emily

PY - 2014

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N2 - We show that the category of algebraically cofibrant objects in a combinatorial and simplicial model category A has a model structure that is left-induced from that on A. In particular, it follows that any presentable model category is Quillen equivalent (via a single Quillen equivalence) to one in which all objects are cofibrant.

AB - We show that the category of algebraically cofibrant objects in a combinatorial and simplicial model category A has a model structure that is left-induced from that on A. In particular, it follows that any presentable model category is Quillen equivalent (via a single Quillen equivalence) to one in which all objects are cofibrant.

KW - Coalgebra

KW - Cofibrant object

KW - Model category

UR - https://www.scopus.com/pages/publications/84985993514

U2 - 10.4310/HHA.2014.v16.n2.a9

DO - 10.4310/HHA.2014.v16.n2.a9

M3 - Article

AN - SCOPUS:84985993514

SN - 1532-0073

VL - 16

SP - 171

EP - 184

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

IS - 2

ER -

Coalgebraic models for combinatorial model categories

Abstract

Keywords

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