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:
Non ci sono file associati a questo prodotto.