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Building on the work of Gerstenhaber and Schack, we define the Hochschild complex of a
presheaf (or a pseudofunctor) on a category as the Hochschild complex of an associated “ …

In this monograph, we extend S. Schwede's exact sequence interpretation of the
Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories …

This paper continues the development of the deformation theory of abelian categories
introduced in a previous paper by the authors. We show first that the deformation theory of …

All notation and conventions are from our notes on Derived Categories (DTC) or Derived
Categories of Sheaves (DCOS). In particular we assume that every abelian category comes …

We develop some new aspects of cohomology in the context of semi-abelian categories: we
establish a Hochschild–Serre 5-term exact sequence extending the classical one for groups …

The notion of exact category is one of the most interesting notion studied in category theory.
In fact, several important mathematical situations can be axiomatized in categorical terms as …

We define the normal Hochschild cohomology of an admissible subcategory of the derived
category of coherent sheaves on a smooth projective variety X, a graded vector space which …

These notes aim to complement the lecture notes of Caldararu by providing an introduction
to explicit methods in the study of derived categories in algebraic geometry. The bounded …

The notion of Hochschild cochains induces an assignment from $\mathsf {Aff} $, affine DG
schemes, to monoidal DG categories. We show that this assignment extends, under …