A Hochschild Cohomology Comparison Theorem for prestacks

TL;DR

This paper generalizes a cohomology comparison theorem to prestacks over small categories, establishing a fully faithful functor between derived categories of bimodules without requiring the base category to be a poset.

Contribution

It extends Gerstenhaber and Schack's theorem to more general prestacks, removing the poset assumption and clarifying the relationship between cohomologies.

Findings

Established a fully faithful functor between derived categories of bimodules

Generalized the cohomology comparison theorem to prestacks over small categories

Removed the need for the base category to be a poset

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 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 U is a poset.