相关论文: Tannakian categories: origins and summary

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills…

We summarize some of the main ideas and results around symplectic field theory, from its early inception up to recent and ongoing developments.

In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…

We consider the origins of Higher Tannaka duality, as well as it consequences. In a first time we review the work of J. Wallbridge on that subject, which shows in particular that Hopf algebras are essential to generating Tannakian…

This text is dedicated to the development of the theory of $(\infty,\omega)$-categories. We present generalizations of standard results from category theory, such as the lax Grothendieck construction, the Yoneda lemma, lax (co)limits and…

These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.

A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…

We introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. The aim of the paper is to justify and contextualize the new notion by…

We give a short introduction to category theory aimed at philosophers. We emphasize methodological issues and philosophical ramifications.

This should be the final version of this paper. Numberous minor improvements have been made to the manuscript, one argument has been corrected, and an appendix has been added.

We give a presentation of Feynman categories from a representation--theoretical viewpoint. Feynman categories are a special type of monoidal categories and their representations are monoidal functors. They can be viewed as a far reaching…

In this article, the theory of sheaves is studied from a categorical point of view. This perspective vastly generalizes the usual theory of sheaves of sets to a more abstract setting which allows us to investigate the theory of sheaves with…

We give an introduction to the theory of cluster categories and cluster tilted algebras. We include some background on the theory of cluster algebras, and discuss the interplay with cluster categories and cluster tilted algebras.

We introduce basic notions in category theory to type theorists, including comprehension categories, categories with attributes, contextual categories, type categories, and categories with families along with additional discussions that are…

This is a condensed overview of the formal theory of monads in a 2-category. We also define two double categories of monads in a 2-category, extending Lack and Street's 2-categories of monads.

Recent advances in computational techniques for $K$-theory allow us to describe the $K$-theory of toric varieties in terms of the $K$-theory of fields and simple cohomological data.

We determine internal characterisations for when a tensor category is (super) tannakian, for fields of positive characteristic. This generalises the corresponding characterisations in characteristic zero by P. Deligne. We also explore…

We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…

Recently, Harman and the second author introduced a new construction of pre-Tannakian tensor categories based on oligomorphic groups. We develop tools for analyzing the Drinfeld centers of these categories, and compute the center explicitly…

Strong similarities have been long observed between the Galois (Categories Galoisiennes) and the Tannaka (Categories Tannakiennes) theories of representation of groups. In this paper we construct an explicit (neutral) Tannakian context for…