Ind-abelian categories and quasi-coherent sheaves

  title={Ind-abelian categories and quasi-coherent sheaves},
  author={Daniel Schappi},
We study the question when a category of ind-objects is abelian. Our answer allows a further generalization of the notion of weakly Tannakian categories introduced by the author. As an application we show that, under suitable conditions, the category of coherent sheaves on the product of two schemes with the resolution property is given by the Deligne tensor product of the categories of coherent sheaves of the two factors. To do this we prove that the class of quasi-compact and semi-separated… 
Tensor products of finitely cocomplete and abelian categories
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
Tensor categorical foundations of algebraic geometry
Tannaka duality and its extensions by Lurie, Sch\"appi et al. reveal that many schemes as well as algebraic stacks may be identified with their tensor categories of quasi-coherent sheaves. In this
Additive Grothendieck pretopologies and presentations of tensor categories.
We define a notion on preadditive categories which plays a role similar to the notion of a Grothendieck pretopology on an unenriched category. Each such additive pretopology defines an additive
Schur Functors and Categorified Plethysm
It is known that the Grothendieck group of the category of Schur functors is the ring of symmetric functions. This ring has a rich structure, much of which is encapsulated in the fact that it is a
Local cohomology sheaves on algebraic stacks
We develop a concept of local cohomology sheaves for algebraic stacks and compare with the classic construction for schemes due to Grothendieck.
Bicategorical colimits of tensor categories
In this expository paper we explain in detail how to construct bicategorical colimits of several kinds of tensor categories, for example essentially small finitely cocomplete K-linear tensor


The resolution property of algebraic surfaces
  • P. Gross
  • Mathematics
    Compositio Mathematica
  • 2011
Abstract We prove that on separated algebraic surfaces every coherent sheaf is a quotient of a locally free sheaf. This class contains many schemes that are neither normal, reduced, quasiprojective
Homotopy theory of comodules over a Hopf algebroid
Given a good homology theory E and a topological space X, the E-homology of X is not just an E_{*}-module but also a comodule over the Hopf algebroid (E_{*}, E_{*}E). We establish a framework for
A Coherent Approach to Pseudomonads
Abstract The formal theory of monads can be developed in any 2-category, but when it comes to pseudomonads, one is forced to move from 2-categories to Gray-categories (semistrict 3-categories). The
Coherence of tricategories
Interestingly, coherence of tricategories that you really wait for now is coming. It's significant to wait for the representative and beneficial books to read. Every book that is provided in better