Revisiting function complexes and simplicial localisation
Category Theory
2014-09-30 v1 Algebraic Topology
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.
Cite
@article{arxiv.1409.8062,
title = {Revisiting function complexes and simplicial localisation},
author = {Zhen Lin Low},
journal= {arXiv preprint arXiv:1409.8062},
year = {2014}
}
Comments
23 pages, LaTeX