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arXiv · 2003.10105

Monoidal abelian envelopes

Kevin Coulembier
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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 tensor categories in positive characteristic via tilting modules for SL(2).

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Kevin Coulembier. 2020-03-23. Monoidal abelian envelopes. https://doi.org/10.1112/s0010437x21007399

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