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arXiv · 2601.16092

Monoidal adjunctions and abelian envelopes

Johannes Flake·Robert Laugwitz·Sebastian Posur
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Abstract

We show how monoidal adjunctions can be used to prove the existence of monoidal abelian envelopes of pseudo-tensor categories, in particular, those admitting a combinatorial description with certain properties. We derive concrete general criteria, which we then demonstrate by giving relatively simple combinatorial proofs of the existence of new abelian envelopes for interpolation categories of the hyperoctahedral and of the modified symmetric groups.

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Johannes Flake, Robert Laugwitz, Sebastian Posur. 2026-03-02. Monoidal adjunctions and abelian envelopes. https://arxiv.org/abs/2601.16092

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