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arXiv · 2107.02374

Homological kernels of monoidal functors

Kevin Coulembier
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Abstract

We show that each rigid monoidal category A over a field defines a family of universal tensor categories, which together classify all faithful monoidal functors from A to tensor categories. Each of the universal tensor categories classifies monoidal functors of a given 'homological kernel' and can be realised as a sheaf category, not necessarily on A. This yields a theory of 'local abelian envelope' which completes the notion of monoidal abelian envelopes.

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Kevin Coulembier. 2021-07-06. Homological kernels of monoidal functors. https://arxiv.org/abs/2107.02374

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