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Monoidal abelian envelopes

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arxiv 2003.10105 v2 pith:ZJTXC333 submitted 2020-03-23 math.CT math.RT

Kevin Coulembier This is my paper · ORCID
classification math.CTmath.RT
keywords categoriestensorabelianenvelopesexampleexistencemonoidalanother
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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).

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories

    math.QA 2025-06 accept novelty 8.0 of 10

    A finite braided tensor category is fully dualizable in the Morita 4-category of braided pre-tensor categories whenever its symmetric center is separable.

  2. Classical interpolation categories

    math.RT 2025-07 conditional novelty 7.0 of 10

    Ultraproduct and oligomorphic-group constructions of interpolation categories for finite classical groups agree, and the categories depend only on a parameter t, with an additional parity label in the orthogonal case.

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