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Cocycles in categories of fibrant objects

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arxiv 1502.03925 v3 pith:7JKPXTWX submitted 2015-02-13 math.CT math.AT

Zhen Lin Low This is my paper · ORCID
classification math.CTmath.AT
keywords fibrantobjectscalculuscategorycocycleshomotopicaladmitsapplication
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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.

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  1. Shifted symplectic structures on derived Quot-stacks I: Differential graded manifolds

    math.AG 2019-08 conditional novelty 7.0 of 10

    Dg manifolds form a homotopy site whose infinity category of stacks is equivalent to the Toen-Vezzosi category of stacks on dg algebras with finitely many generators in each degree.

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