Hochschild cohomology in toposes
Category Theory
2024-03-14 v1 Logic
Rings and Algebras
Abstract
We develop a theory of internal Hochschild cohomology in a ringed topos. We construct it via the internal Hochschild cochain complex, as well as through derived functor/topos cohomology theory, and discuss its relationship to the absolute Hochschild cohomology. By specialising to the topos of difference sets, we obtain a theory of internal difference Hochschild cohomology, and compare it to the absolute Hochschild cohomology through the Grothendieck and hypercohomology spectral sequences. We provide a systematic and detailed treatment of tensor products in suitable toposes in hope to complete the existing literature.
Cite
@article{arxiv.2403.08087,
title = {Hochschild cohomology in toposes},
author = {Cameron Michie and Ivan Tomasic},
journal= {arXiv preprint arXiv:2403.08087},
year = {2024}
}