Cohomology of exact categories and (non-)additive sheaves

  title={Cohomology of exact categories and (non-)additive sheaves},
  author={Dmitry Kaledin and Wendy Lowen},
  journal={Advances in Mathematics},
What do Abelian categories form?
  • D. Kaledin
  • Mathematics
    Russian Mathematical Surveys
  • 2022
Given two finitely presentable Abelian categories and , we outline a construction of an Abelian category of functors from to , which has nice 2-categorical properties and provides an explicit model
On the tensor product of linear sites and Grothendieck categories
We define a tensor product of linear sites, and a resulting tensor product of Grothendieck categories based upon their representations as categories of linear sheaves. We show that our tensor product
Cycles over DGH-semicategories and pairings in categorical Hopf-cyclic cohomology
Let $H$ be a Hopf algebra and let $\mathcal D_H$ be a Hopf-module category. We describe the cocycles and coboundaries for the Hopf cyclic cohomology of $\mathcal D_H$, which correspond respectively
Hochschild cohomology and deformations of $\mathbb{P}$-functors
Given a split $\mathbb{P}$-functor $F:\mathcal{D}^b(X) \to \mathcal{D}^b(Y)$ between smooth projective varieties, we provide necessary and sufficient conditions, in terms of the Hochschild cohomology
Exact structures and degeneration of Hall algebras
Bokstein homomorphism as a universal object
N-Quasi-Abelian Categories vs N-Tilting Torsion Pairs
Rump and successively Bondal and Van den Bergh provide an equivalence between the notion of quasi-abelian category studied by Schneiders and that of tilting torsion pair on an abelian category. Any
On the obscure axiom for one-sided exact categories
One-sided exact categories are obtained via a weakening of a Quillen exact category. Such one-sided exact categories are homologically similar to Quillen exact categories: a one-sided exact category


Hochschild homology and Gabber's Theorem
Gabber's Theorem claims that the singular support of a D-module is involutive. We show how to give a conceptually clear proof of this in the context of Hochschild Homology and Cohomology of abelian
We define a notion of a strong homotopy BV algebra and apply it to deformation theory problems. Formality conjectures for Hochschild cochains are formulated. We prove several results supporting these
The spectrum of a locally coherent category
Compatibility, Stability, and Sheaves
The focus of this book is to construct an appropriate setting in which to do algebraic geometry over noncommutative noetherian rings. The principal tool of “modern” algebraic geometry is the
On differential graded categories
Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by
Comparison of MacLane, Shukla and Hochschild cohomologies
It is known that MacLane cohomology coincides with topological Hochschild cohomology ([28]) and coincides also with Baues-Wirsching cohomology of the category of finitely generated free A-modules
Deformation theory of abelian categories
In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the well-known deformation theory of algebras developed by
A generalization of the Gabriel–Popescu theorem
Hochschild cohomology of abelian categories and ringed spaces
Higher Topos Theory
This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the