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B\in {\mathcal {C}}} . A braided monoidal category is a monoidal category C {\displaystyle {\mathcal {C}}} equipped with a braiding—that is, a commutativity...

In mathematics, a monoidal category (or tensor category) is a category C {\displaystyle \mathbf {C} } equipped with a bifunctor ⊗ : C × C → C {\displaystyle...

In category theory, a branch of mathematics, a symmetric monoidal category is a monoidal category (i.e. a category in which a "tensor product" ⊗ {\displaystyle...

in category theory, a closed monoidal category (or a monoidal closed category) is a category that is both a monoidal category and a closed category in...

is a monoidal functor whose coherence maps are identities. A braided monoidal functor is a monoidal functor between braided monoidal categories (with...

Closed monoidal category Braided monoidal category Topos Category of small categories Semigroupoid Comma category Localization of a category Enriched...

Artin–Tits group Braided monoidal category Braided vector space Braided Hopf algebra Knot theory Non-commutative cryptography Spherical braid group Weisstein...

In mathematics a Yetter–Drinfeld category is a special type of braided monoidal category. It consists of modules over a Hopf algebra which satisfy some...

given by the tensor product. The category Z ( C ) {\displaystyle {\mathcal {Z(C)}}} becomes a braided monoidal category with the tensor product on objects...

of braided monoidal categories were found in rational conformal field theory. Tannaka–Krein philosophy suggests that braided monoidal categories arising...

algebra is naturally extended to arbitrary braided monoidal categories. A Hopf algebra in such a category ( C , ⊗ , I , α , λ , ρ , γ ) {\displaystyle...

mathematics, a ribbon category, also called a tortile category, is a particular type of braided monoidal category. A monoidal category C {\displaystyle {\mathcal...

In mathematics, a braided Hopf algebra is a Hopf algebra in a braided monoidal category. The most common braided Hopf algebras are objects in a Yetter–Drinfeld...

right duals. When C is braided (or symmetric), every left dual is also a right dual, and vice versa. If we consider a monoidal category as a bicategory with...

index notation Angular momentum diagrams (quantum mechanics) Braided monoidal category Categorical quantum mechanics uses tensor diagram notation Matrix...

In category theory, a branch of mathematics, a PROP is a symmetric strict monoidal category whose objects are the natural numbers n identified with the...

using braided monoidal category methods one has a natural q-version of this defined here for real values of q {\displaystyle q} as a 'braided hermitian...

x_{j})=q_{ij}(x_{j}\otimes x_{i})} A good source for braided vector spaces entire braided monoidal categories with braidings between any objects τ V , W {\displaystyle...

representing morphisms in monoidal categories, or more generally 2-cells in 2-categories. They are a prominent tool in applied category theory. When interpreted...

{E}}_{n}} -algebra in categories is a monoidal category if n = 1, a braided monoidal category if n = 2, and a symmetric monoidal category if n ≥ 3. If Λ is...