Dwyer-kan localization revisited

Vladimir Hinich

doi:10.4310/HHA.2016.v18.n1.a3

Dwyer-kan localization revisited

Vladimir Hinich

Department of Mathematics

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

Abstract

A version of Dwyer-Kan localization in the context of ∞- categories and simplicial categories is presented. Some results of the classical papers [DK1, DK2, DK3] are reproven and generalized. We prove that a Quillen pair of model categories gives rise to an adjoint pair of their DK localizations (considered as ∞-categories). We study families of ∞-categories and present a result on localization of a family of ∞-categories. This is applied to localization of symmetric monoidal ∞-categories where we were able to get only partial results.

Original language	English
Pages (from-to)	27-48
Number of pages	22
Journal	Homology, Homotopy and Applications
Volume	18
Issue number	1
DOIs	https://doi.org/10.4310/HHA.2016.v18.n1.a3
State	Published - 2016

Bibliographical note

Publisher Copyright:
© 2016, Vladimir Hinich.

Keywords

DK localization
Infinity-category

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.4310/HHA.2016.v18.n1.a3

Cite this

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AB - A version of Dwyer-Kan localization in the context of ∞- categories and simplicial categories is presented. Some results of the classical papers [DK1, DK2, DK3] are reproven and generalized. We prove that a Quillen pair of model categories gives rise to an adjoint pair of their DK localizations (considered as ∞-categories). We study families of ∞-categories and present a result on localization of a family of ∞-categories. This is applied to localization of symmetric monoidal ∞-categories where we were able to get only partial results.

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Dwyer-kan localization revisited

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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