English

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.)