Examples of UFCA in a sentence
Dualizability The calculations in the remainder of this sec- tion utilize the graphical calculus for 3-categories from [BMS12], which applies to weak 3-categories by [Gut19]; in particular, we work in the 3-category UFCA, which satisfies important finiteness, semisim- plicity, and dualizability conditions as it is a full 3- subcategory of a hom 3-category in UBFC.34There are 2D and 3D diagrams drawn in this section.
It is therefore natural to wonder if the 4-category UBFC is somehow related to a 3-category of (2+1)D topo- logical orders.In § II A and (15), we saw that the categorical data which determine commuting projector models for (2+1)D bulk topological orders and (1+1)D do- main walls between them, i.e. data in UFCA, are mathematically interchangeable with the tensor cat- egories describing bulk and wall excitations, which are their counterparts in UBFC.A precise formulation of this statement is as fol- lows.
Decomposability of the composition of 1- morphisms in UFCA means that there are 2- morphisms, i.e. -balanced bimodule functors, which project onto individual summands.
It is natural that (2+1)D topological orders should form a 3-category, where objects are (2+1)D bulk topological orders,image, and by Example II.3, everything in UMTC≤1≤1Aappears in the image of UFCA for some .