Realizable homotopy colimits
Algebraic Geometry
2012-02-17 v3 Algebraic Topology
Category Theory
K-Theory and Homology
Abstract
In this paper we prove that for any model category, the Bousfield-Kan construction of the homotopy colimit is the absolute left derived functor of the colimit. This is achieved by showing that the Bousfield-Kan homotopy colimit is moreover a realizable homotopy colimit, defined by means of a suitable 2-category of relative categories. In addition, in the case of exact coproducts, we characterize the realizable homotopy colimits that satisfy a cofinality property as those given by a formula following the pattern of Bousfield-Kan construction: they are the composition of a "geometric realization" with the simplicial replacement.
Cite
@article{arxiv.1104.0646,
title = {Realizable homotopy colimits},
author = {Beatriz Rodriguez Gonzalez},
journal= {arXiv preprint arXiv:1104.0646},
year = {2012}
}
Comments
34 pages; some results generalized and the presentation is improved