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 …

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 study abelian envelopes for pseudo-tensor categories with the property that every object
in the envelope is a quotient of an object in the pseudo-tensor category. We establish an …

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 …

We apply the recently introduced notion, due to Dyckerhoff, Kapranov, and Schechtman, of-
spherical functors of stable infinity categories, which generalise spherical functors, to the …

We develop theory and examples of monoidal functors on tensor categories in positive
characteristic that generalise the Frobenius functor from\cite {Os, EOf, Tann}. The latter has …