The center functor is fully faithful

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.

25 pages, more details are added, some typos are fixed

References in corpus (2)

• Integrating quantum groups over surfaces
• Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers

Cited by in corpus (28)

• Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries
• Boundary-bulk relation in topological orders
• Classification of topological phases with finite internal symmetries in all dimensions
• A mathematical theory of gapless edges of 2d topological orders. Part I
• Gapless edges of 2d topological orders and enriched monoidal categories
• Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers
• A mathematical theory of gapless edges of 2d topological orders. Part II
• Categories of quantum liquids I
• A topological phase transition on the edge of the 2d ${\mathbb{Z}}_2$ topological order
• Composing topological domain walls and anyon mobility
• Topological orders and factorization homology
• Pointed Drinfeld center functor
• Domain walls between 3d phases of Reshetikhin-Turaev TQFTs
• Categories of quantum liquids II
• Extended TQFT arising from enriched multi-fusion categories
• Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model
• Realization of rigid C*-bicategories as bimodules over type II${}_1$ von Neumann algebras
• Category of SET orders
• Quantum Statistical Mechanics of the Absolute Galois Group
• Enriched monoidal categories I: centers
• Categorical descriptions of one-dimensional gapped phases with Abelian onsite symmetries
• Semisimple and separable algebras in multi-fusion categories
• The Symmetry Enriched Center Functor is Fully Faithful
• A field guide to categories with $A_n$ fusion rules
• Dualities between 2+1d fusion surface models from braided fusion categories
• Categorical computation
• Graded character sheaves, HOMFLY-PT homology, and Hilbert schemes of points on ${\mathbb{C}}^2$
• Separable algebras in multitensor C${}^{\ast }$-categories are unitarizable