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- W4384389949 abstract "We develop a general theory of 3-dimensional ``orbifold completion'', to describe (generalised) orbifolds of topological quantum field theories as well as all their defects. Given a semistrict 3-category $mathcal{T}$ with adjoints for all 1- and 2-morphisms (more precisely, a Gray category with duals), we construct the 3-category $mathcal{T}_{textrm{orb}}$ as a Morita category of certain $E_1$-algebras in $mathcal{T}$ which encode triangulation invariance. We prove that in $mathcal{T}_{textrm{orb}}$ again all 1- and 2-morphisms have adjoints, that it contains $mathcal{T}$ as a full subcategory, and we argue that it satisfies a universal property which implies $(mathcal{T}_{textrm{orb}})_{textrm{orb}} cong mathcal{T}_{textrm{orb}}$. This is a categorification of the work in [CR]. Orbifold completion by design allows us to lift the orbifold construction from closed TQFT to the much richer world of defect TQFTs. We illustrate this by constructing a universal 3-dimensional state sum model with all defects from first principles, and we explain how recent work on defects between Witt equivalent Reshetikhin--Turaev theories naturally appears as a special case of orbifold completion." @default.
- W4384389949 created "2023-07-15" @default.
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- W4384389949 date "2023-07-12" @default.
- W4384389949 modified "2023-09-25" @default.
- W4384389949 title "Orbifold completion of 3-categories" @default.
- W4384389949 doi "https://doi.org/10.48550/arxiv.2307.06485" @default.
- W4384389949 hasPublicationYear "2023" @default.
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