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arXiv · 2104.07747

A Characterization of Braided Enriched Monoidal Categories

Zachary Dell
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Abstract

We construct an equivalence between the 2-categories VMonCat of rigid V-monoidal categories for a braided monoidal category V and VModTens of oplax braided functors from V into the Drinfeld centers of ordinary rigid monoidal categories. The 1-cells in each are the respective lax monoidal functors, and the 2-cells are the respective monoidal natural transformations. Our proof also gives an equivalence in the case that we consider only strong monoidal 1-cells on both sides. The 2-categories VMonCat and VModTens have G-graded analogues. We also get an equivalence of 2-categories between G-extensions of some fixed V-monoidal category A, and G-extensions of some fixed V-module tensor category (A, F_A^Z).

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Zachary Dell. 2021-04-15. A Characterization of Braided Enriched Monoidal Categories. https://arxiv.org/abs/2104.07747

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