Fusion 2-categories and a state-sum invariant for 4-manifolds

By Christopher L. Douglas, David J. Reutter. 2018

156 citations recorded by the source corpus.

We introduce semisimple 2-categories, fusion 2-categories, and spherical fusion 2-categories. For each spherical fusion 2-category, we construct a state-sum invariant of oriented singular piecewise-linear 4-manifolds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2388ec221738c815b14e8629390e9edee2314fb2

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Universal Non‐Invertible Symmetries (2022, methodology): “Moreover, since BT is a braided fusion category, the 2-category Mod(BT) carries a monoidal structure and forms a fusion 2-category [17].”
Symmetries and strings of adjoint QCD2 (2020, background): “Moreover, surface operators in the 3d TQFT form a 2-category [46, 48, 50, 106] and the fusion between algebras defined in (5.”
Higher Gauging and Non-invertible Condensation Defects (2022, methodology): “cases of our fusion rules for the condensation surfaces were computed in the context of fusion 2-category [59] in [60] (see also [61]).”
Braided Picard groups and graded extensions of braided tensor categories (2020, background): “Namely, it 1 For fusion categories, these 2-categories of module categories are fusion 2-categories [16].”
Q-system completion for C⁎ 2-categories (2021, unknown): “Given a C ∗ / W ∗ 2-category C , its Q-system completion is the 2-category QSys ( C ) of Q-systems, bimodules, and intertwiners in C , which has been studied previously in [NY16, BKLR15, GY20], building on algebraic versions in [Yam04a, CR16, DR18, GJF19].”