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

Abstract

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.

References in corpus (12)

• String-net condensation: A physical mechanism for topological phases
• Quantum computation with Turaev-Viro codes
• Modular categories as representations of the 3-dimensional bordism 2-category
• A categorical construction of 4D TQFTs
• On braided fusion categories I
• Dichromatic state sum models for four-manifolds from pivotal functors
• State-Sum Invariants of 4-Manifolds I
• Categorified trace for module tensor categories over braided tensor categories
• Representation theory of 2-groups on finite dimensional 2-vector spaces
• From Subfactors to Categories and Topology I. Frobenius algebras in and Morita equivalence of tensor categories
• Beyond Anyons
• A note on separable functors and monads

Cited by in corpus (54)

• Universal Non-Invertible Symmetries
• Unifying Constructions of Non-Invertible Symmetries
• Non-Invertible Symmetry Webs
• Non-invertible Symmetries and Higher Representation Theory I
• On lattice models of gapped phases with fusion category symmetries
• Classification of topological phases with finite internal symmetries in all dimensions
• Higher categorical symmetries and gauging in two-dimensional spin systems
• Non-invertible Symmetries and Higher Representation Theory II
• The center of monoidal 2-categories in 3+1D Dijkgraaf-Witten Theory
• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Minimal nondegenerate extensions
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Higher-group symmetry in finite gauge theory and stabilizer codes
• Topological holography, quantum criticality, and boundary states
• Absolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions
• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
• Q-system completion for C* 2-categories
• Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
• Fusion 2-categories with no line operators are grouplike
• Composing topological domain walls and anyon mobility
• String Condensations in 3+1D and Lagrangian Algebras
• Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part I
• Higher-group symmetry of (3+1)D fermionic ${\mathbb{Z}}_2$ gauge theory: logical CCZ, CS, and T gates from higher symmetry
• Multifusion Categories and Finite Semisimple 2-Categories
• Non-invertible topological defects in 4-dimensional ${\mathbb{Z}}_2$ pure lattice gauge theory
• Gravitational Solitons and Completeness
• Condensations in higher categories
• (3+1)D topological orders with only a ${\mathbb{Z}}_2$-charged particle
• On tensor network representations of the (3+1)d toric code
• Uniqueness of unitary structure for unitarizable fusion categories
• Boundary SymTFT
• A covariant Stinespring theorem
• Finite Semisimple Module 2-Categories
• A 3-categorical perspective on G-crossed braided categories
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Representations of Motion Groups of Links via Dimension Reduction of TQFTs
• The 2-Deligne Tensor Product
• Crossing with the circle in Dijkgraaf-Witten theory and applications to topological phases of matter
• Gauging Categorical Symmetries in 3d Topological Orders and Bulk Reconstruction
• Compact Semisimple 2-Categories
• Local Modules in Braided Monoidal 2-Categories
• Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• Q-system completion is a 3-functor
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• On the Dualizability of Fusion 2-Categories
• Dualities between 2+1d fusion surface models from braided fusion categories
• Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd)
• Fermionic defects of topological phases and logical gates
• Les Houches Lecture Notes on Tensor Networks
• 4-Manifold Invariants From Hopf Algebras
• Fusion of Low-Entanglement Excitations in 2D Toric Code
• Separable algebras in multitensor C${}^{\ast }$-categories are unitarizable
• A universal state sum