Derived Morita theory and Hochschild Homology and Cohomology of DG Categories German Stefanich In this talk we will explore the idea that an algebra Aover a eld (ring, spectrum) kcan be thought of as a way of encoding a category, namely A-mod its category of modules. And. which is zeroin degreep ≤ −apartmanibeogradnadan.com cohomologyofthis complex is the Hochschild cohomology of C, and will be denoted HH• dg (C). We will also need the Hochschild cohomology of an abelian category A. This is not the Hochschild cohomology of this abelian category considered as a k-linear category giving rise to a dg category in degree 0. An Introduction to the Representations and Cohomology of Categories Peter Webb School of Mathematics, University of Minnesota, Minneapolis MN , USA email: [email protected] Contents: 1. Introduction 2. The category algebra and some preliminaries 3. Restriction and induction of representations 4. Parametrization of simple and projective.
Hochschild cohomology of a category of dataCompared to the existing texts these notes aim to focus more on Hochschild (co) homology in algebraic geometry, using derived categories of. The main objective of this paper is to present a theory for computing the Hochschild cohomology of algebras built on a specific data, namely multi- extension. An intrinsic first order deformation theory for abelian categories was developed in , and a notion of Hochschild cohomology was defined in. It's the self-Ext algebra of the identity functor from the category to itself. So, for an algebra, this reduces to the self-Ext algebra of the diagonal. Hochschild cohomology and the centre of the derived category. 17 .. We keep track of these additional data through the following notation. cohomology) should be defineable just in terms of the category, independent of Our end goal is to say what it means to take the Hochschild homology and . determined from the data of F(A), which is an object of B -mod with an Aop action. of C with respect to S is the data of a category S−1C and a functor l: C −→ S .. complex of (R,R)-bi-modules induces a map on K-theory, Hochschild homology. structure preserving functors between exact monoidal categories. We use . Hochschild cohomology for abelian categories. by the data. Keywords: recollement, smoothness, Hochschild cohomology. recollements are derived categories of algebras, which are closely related to and M. Saorin , Parametrizing recollement data for triangulated categories. It has multiple interpretations in higher category theory. Presently, everything below pertains to Hochschild homology of commutative algebras;.
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