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Monoidal abelian envelopes
- Part of
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- Journal:
- Compositio Mathematica / Volume 157 / Issue 7 / July 2021
- Published online by Cambridge University Press:
- 24 June 2021, pp. 1584-1609
- Print publication:
- July 2021
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- Article
- Export citation
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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 interesting tensor categories in positive characteristic via tilting modules for
${\rm SL}_2$.
