Monoidal abelian envelopes

Abstract

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 example we obtain new proofs for the existence of several universal tensor categories as conjectured by Deligne. Another example constructs tensor categories in positive characteristic via tilting modules for SL(2).

References in corpus (2)

• Tannakian categories in positive characteristic
• Finite symmetric integral tensor categories with the Chevalley property

Cited by in corpus (3)

• Semi-infinite highest weight categories
• Lectures on Symmetric Tensor Categories
• Monoidal abelian envelopes and a conjecture of Benson--Etingof