Revisiting function complexes and simplicial localisation

Abstract

In this paper three results are established: firstly, that the homotopy function complexes of Dwyer and Kan can be defined as certain total right derived functors; secondly, that they functorially compute the homotopy type of the hom-spaces in the simplicial localisation; and thirdly, that they can be computed by fibrant replacements in a suitable left Bousfield localisation of the projective model structure on simplicial presheaves.

23 pages, LaTeX

Cited by in corpus (1)

• Model $\infty$-categories I: some pleasant properties of the $\infty$-category of simplicial spaces