Hochschild Cohomology, Monoid Objects and Monoidal Categories
Category Theory
2022-01-25 v1 Algebraic Topology
K-Theory and Homology
Abstract
This paper expands further on a category theoretical formulation of Hochschild cohomology for monoid objects in monoidal categories enriched over abelian groups, which has been studied in arXiv:1605.00842. This topic was also presented at ISCRA, Isfahan, Iran, April 2019. The present paper aims to provide a more intuitive formulation of the Hochschild cochain complex and extend the definition to Hochschild cohomology with values in a bimodule object. In addition, an equivalent formulation of the Hochschild cochain complex in terms of a cosimplicial object in the category of abelian groups is provided.
Cite
@article{arxiv.2201.09401,
title = {Hochschild Cohomology, Monoid Objects and Monoidal Categories},
author = {Magnus Hellstrøm-Finnsen},
journal= {arXiv preprint arXiv:2201.09401},
year = {2022}
}
Comments
12 pages