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Monoidal abelian envelopes

Part of: Categories and geometry Categories with structure Linear algebraic groups and related topics

Published online by Cambridge University Press:  24 June 2021

Kevin Coulembier
Kevin Coulembier*
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australiakevin.coulembier@sydney.edu.au
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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 interesting tensor categories in positive characteristic via tilting modules for ${\rm SL}_2$.

Keywords

tensor categoryuniversal monoidal categoryabelian envelopetilting module

MSC classification

Primary: 18D15: Closed categories (closed monoidal and Cartesian closed categories, etc.) 18F20: Presheaves and sheaves 18F10: Grothendieck topologies 20G05: Representation theory
Type
Research Article
Information
Compositio Mathematica , Volume 157 , Issue 7 , July 2021 , pp. 1584 - 1609
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Copyright
© 2021 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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