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Fusion 2-categories with no line operators are grouplike
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abstract
We show that if $\mathcal{C}$ is a fusion $2$-category in which the endomorphism category of the unit object is $\rm{Vec}$ or $\rm{SVec}$, then the indecomposable objects of $\mathcal{C}$ form a finite group.
Forward citations
Cited by 4 Pith papers
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Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism
For G=(Z2,Z2,triv,1), the authors classify anomalies via oriented and spin bordism in spacetime dimensions d<=5 and derive the (3+1)D SymTFT boundary conditions, including the equivalence of the anomalous symmetry cat...
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The Classification of 3+1d Symmetry Enriched Topological Order
Finite-group-enriched 3+1d topological orders are classified by 2SVect-enriched G-crossed braided fusion 2-categories, with gauging obstructions living in SW^5(BG).
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Compact Semisimple Tensor 2-Categories are Morita Connected
Every compact semisimple tensor 2-category is Morita equivalent to a connected one over arbitrary fields of characteristic zero, with applications to Witt groups and Galois cohomology.
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Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories
Non-invertible symmetries in finite-group gauge theories are realized as condensation defects, with a complete Z_N dictionary and new automorphism symmetry expressions.
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