相关论文: Tannakian categories: origins and summary

We classify the "quotients" of a tannakian category in which the objects of a tannakian subcategory become trivial, and we examine the properties of such quotient categories.

We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples

It has long been said that the theories of Galois and Tannakian categories over a field $k$ are just ``formally similar''. With this note I will argue that this is in fact not the case: not only do Tannakian categories generalize Galois…

We study several classes of braided fusion categories, and prove that they all contain nontrivial Tannakian subcategories. As applications, we classify some fusion categories in terms of solvability and group-theoreticality.

Pre-Tannakian categories are a natural class of tensor categories that can be viewed as generalizations of algebraic groups. We define a pre-Tannkian category to be discrete if it is generated by an \'etale commutative algebra; these…

We introduce a notion of fine Tannakian infinity-categories and prove Tannakian characterization results for symmetric monoidal stable infinity-categories over a field of characteristic zero. It connects derived quotient stacks with…

The general theory of Grothendieck categories is presented. We systemize the principle methods and results of the theory, showing how these results can be used for studying rings and modules.

We draw the connection between the model theoretic notions of internality and the binding group on one hand, and the Tannakian formalism on the other. More precisely, we deduce the fundamental results of the Tannakian formalism by…

We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.

We consider semisimple super Tannakian categories generated by an object whose symmetric or alternating tensor square is simple up to trivial summands. Using representation theory, we provide a criterion to identify the corresponding…

Drawing on well-known results from the theory of canonical extensions and the theory of categories enriched over a quantale, we define canonical extensions of quantale-enriched categories and establish their basic properties.

We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion of a neutral Tannakian category used to characterize the…

We develop a theory of tensor categories over a field endowed with abstract operators. Our notion of a "field with operators", coming from work of Moosa and Scanlon, includes the familiar cases of differential and difference fields,…

We introduce a notion of $\Theta$-categories, which is a refinement of the notion of symmetric monoidal $\infty$-categories. We use this notion to prove a Tannakian duality statement, relating $\Theta$-categories with fpqc-stacks by means…

Given a semi-simple pre-Tannakian category over a finite field, we show that (a slight modification of) its linearization over a field of characteristic 0 is also semi-simple and pre-Tannakian. The key input is a result of Kuhn on the…

This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…

Starting from certain perverse sheaves on an abelian variety, including the intersection cohomology sheaves of curves and smooth ample divisors, we construct a semisimple super-Tannakian category.

We describe an approach to classification of fusion categories in terms of Morita equivalence. This is usually achieved by analyzing Drinfeld centers of fusion categories and finding Tannakian subcategories therein.

We define a notion of "theory of (1,infty)-categories", and we prove that such a theory is unique up to equivalence.

We prove that the derived categories for toric varieties have complete exceptional collections.