Alphabeta MathNon-Invertible Symmetry Operators and Fusion
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1 · Prerequisites
Abstract Algebra
Advanced QFT and Supersymmetry
Category Theory
- Abelian Categories
- Categories, Functors and Natural Transformations
- Duality and Rigidity in Monoidal Categories
- Limits and Colimits
- Monoidal Categories and Monoidal Functors
- Preadditive and Additive Categories and Biproducts
- Reflective Subcategories and the Adjoint Functor Theorems
- Subobject Lattices Generators and the Grothendieck Axioms
- Tensor and Fusion Categories
Combinatorics
Linear Algebra
Quantum Field Theory Mathematics
Real Analysis
Set Theory
- Cardinal Arithmetic, Cofinality and the Alephs
- Construction of the Natural Numbers
- Order, Zorn's Lemma, and the Axiom of Choice
- Ordinal Arithmetic and the First Uncountable Ordinal
- Ordinals, Cardinals, and Transfinite Recursion
- Relations, Functions, and Quotients
- The ZFC Axioms and the Basic Set Constructions
2 · Logical flowchart
3 · Items
Definition
Skeletal Ising fusion-data package
Lemma
Coherence of the Ising fusion data
Physics theorem
Finite-lattice realization of the Ising non-invertible defect
Sources
- Steven H. Simon, Topological Quantum, §§9.2–9.3
- David Aasen, Roger S. K. Mong, and Paul Fendley, Topological Defects on the Lattice I: The Ising Model
- Jürg Fröhlich, Jürgen Fuchs, Ingo Runkel, and Christoph Schweigert, Kramers–Wannier Duality from Conformal Defects
- Nils Carqueville, Lecture Notes on 2-Dimensional Defect TQFT