Hochschild cohomology and “smoothness” in monoidal categories |
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| Authors: | A Ardizzoni C Menini D ?tefan |
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| Institution: | a University of Ferrara, Department of Mathematics, Via Machiavelli 35, Ferrara, I-44100, Italy
b University of Bucharest, Faculty of Mathematics, Str. Academiei 14, Bucharest, Ro-70109, Romania |
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| 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 ≤1 (formally smooth algebras). Several particular cases and applications are included in the last section of the paper. |
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| Keywords: | primary 16 secondary 16 |
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