Cocycles in categories of fibrant objects
Category Theory
2015-09-29 v3 Algebraic Topology
Abstract
We establish that a category of fibrant objects (in the sense of Brown) admits a Dwyer-Kan homotopical calculus of right fractions. This is done using a homotopical calculus of cocycles, which is an auxiliary structure that can be defined on every category of fibrant objects. As an application, we deduce some non-abelian versions of the Verdier hypercovering theorem.
Keywords
Cite
@article{arxiv.1502.03925,
title = {Cocycles in categories of fibrant objects},
author = {Zhen Lin Low},
journal= {arXiv preprint arXiv:1502.03925},
year = {2015}
}
Comments
36 pages, LaTeX. v3: Fixed errors arising from an incorrect definition of "homotopical calculus of right fractions"; improved exposition. (Note that some numbering has changed.)