A finite braided tensor category is fully dualizable in the Morita 4-category of braided pre-tensor categories whenever its symmetric center is separable.
State-Sum Invariants of 4-Manifolds I
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We provide, with proofs, a complete description of the authors' construction of state-sum invariants announced in [CY], and its generalization to an arbitrary (artinian) semisimple tortile category. We also discuss the relationship of these invariants to generalizations of Broda's surgery invariants [Br1,Br2] using techniques developed in the case of the semi-simple sub-quotient of $Rep(U_q(sl_2))$ ($q$ a principal $4r^{th}$ root of unity) by Roberts [Ro1]. We briefly discuss the generalizations to invariants of 4-manifolds equipped with 2-dimensional (co)homology classes introduced by Yetter [Y6] and Roberts [Ro2], which are the subject of the sequel. (citations refer to bibliography in the paper)
fields
math.QA 1years
2025 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories
A finite braided tensor category is fully dualizable in the Morita 4-category of braided pre-tensor categories whenever its symmetric center is separable.