Cohomology of exact categories and (non-)additive sheaves
Dmitry Kaledin, Wendy Lowen
TL;DR
This paper introduces a new approach to Hochschild cohomology for exact categories using (non-)additive sheaves, providing a unified framework and comparing it with existing definitions.
Contribution
It develops an absolute Hochschild cohomology theory for exact categories via Ext in bisheaf categories, offering a novel perspective.
Findings
Defines Hochschild cohomology for exact categories using bisheaf categories
Establishes connections and comparisons with existing cohomology definitions
Provides a new framework for studying (non-)additive sheaves in this context
Abstract
We use (non-)additive sheaves to introduce an (absolute) notion of Hochschild cohomology for exact categories as Ext's in a suitable bisheaf category. We compare our approach to various definitions present in the literature.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons