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A non-abelian Verdier's hypercovering theorem

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If you have a question about this talk, please contact Dr Ignacio Lopez Franco.

One of the central problems in classical sheaf theory is to compute the sheaf cohomology groups of a given sheaf or presheaf of abelian groups. Under favourable conditions, this can be done using Čech cohomology, and the original version of Verdier’s hypercovering theorem can be seen as a vast generalisation of this.

In the first half of this talk, I will recall the notion of a category of fibrant objects in the sense of Brown and give a homotopy colimit formula for computing the derived hom-spaces in the simplicially enriched case. Then, in the second half, I will apply this to the case of simplicial presheaves on a site to obtain a non-abelian version of Verdier’s hypercovering theorem.

This talk is part of the Category Theory Seminar series.

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