A Hochschild cohomology comparison theorem for prestacks

Lowen, Wendy; Van den Bergh, Michel

doi:10.1090/S0002-9947-2010-05288-2

A Hochschild cohomology comparison theorem for prestacks
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by Wendy Lowen and Michel Van den Bergh PDF

Trans. Amer. Math. Soc. 363 (2011), 969-986 Request permission

Abstract:

We generalize and clarify Gerstenhaber and Schack’s “Special Cohomology Comparison Theorem”. More specifically we obtain a fully faithful functor between the derived categories of bimodules over a prestack over a small category $\mathcal {U}$ and the derived category of bimodules over its corresponding fibered category. In contrast to Gerstenhaber and Schack we do not have to assume that $\mathcal {U}$ is a poset.

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