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;
2007-01-01

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.
2007
208
297
330
http://dx.doi.org/10.1016/j.jpaa.2005.12.003
Hochschild cohomology; monoidal categories; bialgebras.
A. ARDIZZONI; C. MENINI; D. STEFAN
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/93216
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