Hochschild cohomology of ring objects in monoidal categories
Magnus Hellstr{\o}m-Finnsen
TL;DR
This paper extends Hochschild cohomology to ring objects within monoidal categories, establishing a complex, cohomology groups, and demonstrating the graded-commutativity of the cohomology ring.
Contribution
It introduces a definition of Hochschild cohomology for ring objects in monoidal categories and proves its graded-commutative property.
Findings
Defined Hochschild complex and cohomology for ring objects in monoidal categories
Proved the cohomology ring is graded-commutative
Provided interpretations of the cohomology groups
Abstract
We define the Hochschild complex and cohomology of a ring object in a monoidal category enriched over abelian groups. We interpret the cohomology groups and prove that the cohomology ring is graded-commutative.
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