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.
Bibliographical notePublisher Copyright:
© 2016, Vladimir Hinich.
- DK localization
ASJC Scopus subject areas
- Mathematics (miscellaneous)