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- Title
Monoidal abelian envelopes with a quotient property.
- Authors
Coulembier, Kevin; Etingof, Pavel; Ostrik, Victor; Pauwels, Bregje
- 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 햱햾헉 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.
- Subjects
TENSOR products; ABELIAN categories
- Publication
Journal für die Reine und Angewandte Mathematik, 2023, Vol 2023, Issue 794, p179
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2022-0076