Let G be the group of all order-preserving self-maps of the real line. In previous work, the first
two authors constructed a pre-Tannakian category Rep _ (G) associated to G. The present …

A fundamental theorem of P. Deligne (2002) states that a pre-Tannakian category over an
algebraically closed field of characteristic zero admits a fiber functor to the category of …

A symmetric tensor category D over an algebraically closed field k is called incompressible if
its objects have finite length (D is pretannakian) and every tensor functor out of D is an …

We propose a method of constructing abelian envelopes of symmetric rigid monoidal
Karoubian categories over an algebraically closed field k. If char (k)= p> 0, then we use this …

We prove a constructive existence theorem for abelian envelopes of non-abelian monoidal
categories. This establishes a new tool for the construction of tensor categories. As an …

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 …

We develop some foundations of commutative algebra, with a view towards algebraic
geometry, in symmetric tensor categories. Most results establish analogues of classical …

We develop a theory of Frobenius functors for symmetric tensor categories (STC) 𝒞 over a
field 𝒌 of characteristic p, and give its applications to classification of such categories …

This is an expanded version of the notes by the second author of the lectures on symmetric
tensor categories given by the first author at Ohio State University in March 2019 and later at …

We initiate the systematic study of modular representations of symmetric groups that arise
via the braiding in (symmetric) tensor categories over fields of positive characteristic. We …