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 …

We develop axiomatics of highest weight categories and quasi-hereditary algebras in order
to incorporate two semi-infinite situations which are in Ringel duality with each other; the …

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

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 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 …

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 …

arxiv:2311.02264v1 [math.AG] 3 Nov 2023 Page 1 ALGEBRAIC GEOMETRY IN TENSOR
CATEGORIES KEVIN COULEMBIER Abstract. We set up some foundations of generalised …