A finite pre-tensor category is Morita equivalent to a finite tensor category if and only if its Drinfeld center is a finite tensor category.
Modular categories as representations of the 3-dimensional bordism 2-category
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We show that once-extended anomalous 3-dimensional topological quantum field theories valued in the 2-category of k-linear categories are in canonical bijection with modular tensor categories equipped with a square root of the global dimension in each factor.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Defines equivalent P-monoids and L-monoids for S^2 bordisms in Cob(3) that add prime 3-manifold labeled endomorphisms or units to commutative Frobenius monoids, with legs relations forcing simplification to prime unit multiplications in algebras.
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Finite Pre-Tensor Categories that are Morita Equivalent to Finite Tensor Categories
A finite pre-tensor category is Morita equivalent to a finite tensor category if and only if its Drinfeld center is a finite tensor category.
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Topological Field Theories and the Algebraic Structures of the Two-Sphere
Defines equivalent P-monoids and L-monoids for S^2 bordisms in Cob(3) that add prime 3-manifold labeled endomorphisms or units to commutative Frobenius monoids, with legs relations forcing simplification to prime unit multiplications in algebras.