Fusion and multifusion categories

Depends on

• Finite k-linear abelian categories
• Semisimple objects and semisimple abelian categories
• Tensor and multitensor categories

Used by

• Symmetric Rep(Z/2) has singular Hopf-link matrix Counterexample
• Finite semisimple module category over a fusion category Definition
• Fixed-boundary anyonic fusion-path space Definition
• Fixed-charge encoding and code projector Definition
• Fusion rules Definition
• G-graded finite semisimple 2-vector space Definition
• Local anyonic channel projector Definition
• Modular ribbon fusion category and Hopf-link data Definition
• Pointed ribbon categories from abelian 3-cocycles Definition
• RT state spaces from a modular category Definition
• Separable algebra objects and bimodules in a fusion category Definition
• Tensor-invertible objects, fusion-ring units, and invertible operators Definition
• Topological spin Definition
• Unitary fusion category Definition
• A matrix multifusion category with nonsimple unit Example
• Fibonacci fusion data and chiral convention Example
• Finite-dimensional vector spaces form a fusion category Example
• Relative tensor products of bimodules over C times C Example
• A separability idempotent constructs the balanced relative tensor product Lemma
• A uniform rank and action-multiplicity bound for module categories Lemma
• Balancing and the Hopf-link character identity Lemma
• Categorical separability contracts the module deformation complex Lemma
• Distinct fusion-ring characters are orthogonal under duality Lemma
• Fusion paths give a basis of the fixed-boundary path space Lemma
• Fusion-tree basis and dimension recursion Lemma
• Modular Hom state spaces have exact sewing inverses and the dimension formula Lemma
• Module functor adjoints and separable-monad splittings in Mod(C) Lemma
• RT capped operators: geometric Gram factors and exact signature gluing Lemma
• RT handlebody pairings and surgery gluing Lemma
• Simple ribbon fusion dimensions are nonzero Lemma
• The canonical algebra of a fusion category is Frobenius Lemma
• The complete Kirby-color band-slide identity with open colored graph coupons Lemma
• The vacuum F-coefficient records the Frobenius–Schur sign Lemma
• The boundary of the fusion-category development Remark
• Left and right dual objects are isomorphic in a semisimple multitensor category Theorem

Dependency tree · two levels

9 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• Etingof, Gelaki, Nikshych, Ostrik, Tensor Categories, Definition 4.1.1 (standard reference, not scraped)