arXiv subjects

Zachary Dell

Publications and source records attributed to Zachary Dell.

2 recordsLinked to original sources

arXiv2022

Unitary braided-enriched monoidal categories

Braided-enriched monoidal categories were introduced in work of Morrison-Penneys, where they were characterized using braided central functors. Recent work of Kong-Yuan-Zhang-Zheng and Dell extended this characterization to an equivalence of 2-categories. Since their introduction, braided-enriched fusion categories have been used to describe certain phenomena in topologically ordered systems in theoretical condensed matter physics. While these systems are unitary, there was previously no general notion of unitarity for enriched categories in the literature. We supply the notion of unitarity for enriched categories and braided enriched monoidal categories and extend the above 2-equivalence to the unitary setting.

math.CT↗

arXiv2021

A Characterization of Braided Enriched Monoidal Categories

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).

math.CT↗