Monoidal abelian envelopes with a quotient property

Kevin Coulembier, Pavel Etingof, Victor Ostrik, Bregje Pauwels

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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 intrinsic criterion on pseudo-tensor categories for the existence of an abelian envelope satisfying this quotient property. This allows us to interpret the extension of scalars and Deligne tensor product of tensor categories as abelian envelopes, and to enlarge the class of tensor categories for which all extensions of scalars and tensor products are known to remain tensor categories.For an affine group scheme G, we show that pseudo-tensor subcategories of Rep G have abelian envelopes with the quotient property, and we study many other such examples.This leads us to conjecture that all abelian envelopes satisfy the quotient property.
Original languageEnglish
Pages (from-to)179-214
Number of pages36
JournalJournal fur die Reine und Angewandte Mathematik
Volume2023
Issue number794
DOIs
Publication statusPublished - 2023
Externally publishedYes

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