We introduce and investigate the properties of Hochschild cohomology of algebras in an abelian monoidal category M. We show that the second Hochschild cohomology group of an algebra in M classifies extensions of A up to an equivalence. We characterize algebras of Hochschild dimension 0 (separable algebras), and of Hochschild dimension less or equal to 1 (formally smooth algebras). Several particular cases and applications are included in the last section of the paper.
Hochschild Cohomology And 'Smoothness' In Monoidal Categories''
ARDIZZONI, Alessandro;MENINI, Claudia;STEFAN, Dragos
2007
Abstract
We introduce and investigate the properties of Hochschild cohomology of algebras in an abelian monoidal category M. We show that the second Hochschild cohomology group of an algebra in M classifies extensions of A up to an equivalence. We characterize algebras of Hochschild dimension 0 (separable algebras), and of Hochschild dimension less or equal to 1 (formally smooth algebras). Several particular cases and applications are included in the last section of the paper.File in questo prodotto:
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