English

A Characterization of Braided Enriched Monoidal Categories

Category Theory 2021-04-19 v1 Quantum Algebra

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).

Keywords

Cite

@article{arxiv.2104.07747,
  title  = {A Characterization of Braided Enriched Monoidal Categories},
  author = {Zachary Dell},
  journal= {arXiv preprint arXiv:2104.07747},
  year   = {2021}
}

Comments

33 pages, many TikZ diagrams

R2 v1 2026-06-24T01:13:13.132Z