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An $\Infty$-categorical Localisation Functor for Diagrams of Simplicial Sets by Bunk, Severin is a scholarly article available to read on EtoBox.

What is An $\Infty$-categorical Localisation Functor for Diagrams of Simplicial Sets about?

Associated to each small category $C$, there is a category of $C$-shaped diagrams of simplicial sets and an $\infty$-category of $NC$-shaped homotopy coherent diagrams of spaces. We present a functor which exhibits the latter as the $\infty$-categorical localisation of the former at the objectwise weak homotopy equivalences. This builds on a Quillen equivalence between the projective and covariant model structures associated to $C$ due to Heuts-Moerdijk, as well as Cisinski's theory of $\infty$-categorical localisations. We use the localisation functor to give simplified proofs that the left (resp. right) homotopy Kan extension of diagrams of simplicial sets presents the $\infty$-categorical left (resp. right) Kan extension of coherent diagrams of spaces.

Author

Bunk, Severin

Published

2022

Language

EN