Hochschild Cohomology, Monoid Objects and Monoidal Categories
Peer reviewed, Journal article
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Original versionBulletin of the Iranian Mathematical Society (BIMS). 2020 https://doi.org/10.1007/s41980-020-00443-0
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 Hellstrøm-Finnsen (Commun Algebra 46(12):5202–5233, 2018). 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.