Cocycles in categories of fibrant objects

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.

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.)

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