Dwyer-kan localization revisited

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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 languageEnglish
Pages (from-to)27-48
Number of pages22
JournalHomology, Homotopy and Applications
Issue number1
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2016, Vladimir Hinich.


  • DK localization
  • Infinity-category

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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