Simplicial categories II - Dwyer-Kan localizations

Abstract: The goal of this talk will be to understand the idea of localization of a category with respect to the class of maps and see how Dwyer-Kan localization is an example of such. Therefore we will start with the notion of a localization of a category. Then we will proceed to several approaches to the Dwyer-Kan localization - as a derived functor with specific resolution and the hammock version, that gives a constructive description of the homotopy category. We will discuss the relation of DK localization of a simplicial model category and of its homotopy category.

algebraic topologycategory theorygroup theoryK-theory and homology

Audience: researchers in the topic

Cihan Okay

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Recordings of talks available at www.youtube.com/channel/UCLrmyGpqxyeVpTcA1b5HcMw/videos