The center functor is fully faithful

TL;DR

This paper establishes that the Drinfeld center defines a fully faithful functor between certain categories of multi-tensor and braided tensor categories, with applications to topological order physics.

Contribution

It proves the full faithfulness of the center functor for indecomposable multi-fusion categories using physics-inspired methods, providing new proofs of known results.

Findings

Center functor is fully faithful for indecomposable multi-fusion categories.

Provides a mathematical description of boundary-bulk relations in 2+1D topological orders.

Connects category theory with topological order physics.

Abstract

We prove that the notion of Drinfeld center defines a functor from the category of indecomposable multi-tensor categories with morphisms given by bimodules to that of braided tensor categories with morphisms given by monoidal bimodules. Moreover, we apply some ideas from the physics of topological orders to prove that the center functor restricted to indecomposable multi-fusion categories (with additional conditions on the target category) is fully faithful. As byproducts, we provide new proofs to some important known results in fusion categories. In physics, this fully faithful functor gives the precise mathematical description of the boundary-bulk relation for 2+1D anomaly-free topological orders with gapped boundaries.