Geodesic
Dwyer–Kan localization revisited
Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 27-48.

Voir la notice de l'article provenant de la source International Press of Boston

A version of Dwyer–Kan localization in the context of $\infty$-categories and simplicial categories is presented. Some results of the classical papers—“Simplicial localizations of categories” [J. Pure Appl. Algebra 17 (1980), no. 3, 267–284], “Calculating simplicial localizations” [J. Pure Appl. Algebra 18 (1980), no. 1, 17–35], and “Function complexes in homotopical algebra” [Topology 19 (1980), no. 4, 427–440]—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 $\infty$-categories). We study families of $\infty$-categories and present a result on localization of a family of $\infty$-categories. This is applied to localization of symmetric monoidal $\infty$-categories where we were able to get only partial results.
DOI : 10.4310/HHA.2016.v18.n1.a3
Classification : 18D20, 55U35
Keywords: DK localization, infinity-category 
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Vladimir Hinich. Dwyer–Kan localization revisited. Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 27-48. doi : 10.4310/HHA.2016.v18.n1.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n1.a3/

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