We review old and new results concerning the DS functor and associated varieties for Lie
superalgebras. These notions were introduced in the unpublished manuscript (Duflo and …

Given an oligomorphic group $ G $ and a measure $\mu $ for $ G $(in a sense that we
introduce), we define a rigid tensor category $\underline {\mathrm {Perm}}(G;\mu) $ 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 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 …

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 …

We construct and study a nested sequence of finite symmetric tensor categories Vec= C 0⊂
C 1⊂⋯⊂ C n⊂⋯ over a field of characteristic 2 such that C 2 n are incompressible, ie, do …

This book originated from graduate topics courses given by the first author at Yale University
and at the University of California, Berkeley. Since then, the exposition has grown to include …

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 …