Double categories unify modular functors from string-nets and CFT correlators, with a vertical transformation between bicategories shown equivalent, implying field functors are equivalences and universal correlators are isomorphisms.
Bartlett,Three-dimensional TQFTs via string-nets and two-dimensional surgery, preprintmath.QA/2206.13262 [BW] A
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Modular functors and CFT correlators via double categories
Double categories unify modular functors from string-nets and CFT correlators, with a vertical transformation between bicategories shown equivalent, implying field functors are equivalences and universal correlators are isomorphisms.