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Hochschild Cohomology for Functors on Linear Symmetric Monoidal Categories by Romero, Nadia is a scholarly article available to read on EtoBox.

What is Hochschild Cohomology for Functors on Linear Symmetric Monoidal Categories about?

Let $R$ be a commutative ring with unit. We develop a Hochschild cohomology theory in the category $\mathcal{F}$ of linear functors defined from an essentially small symmetric monoidal category enriched in $R$-Mod, to $R$-Mod. The category $\mathcal{F}$ is known to be symmetric monoidal too, so one can consider monoids in $\mathcal{F}$ and modules over these monoids, which allows for the possibility of a Hochschild cohomology theory. The emphasis of the article is in considering natural hom constructions appearing in this context. These homs, together with the abelian structure of $\mathcal{F}$ lead to nice definitions and provide effective tools to prove the main properties and results of the classical Hochschild cohomology theory.

Author

Romero, Nadia

Published

2023

Language

EN