Monoidal categories

category admitting tensor products

bialgebra that admits an antipode

In mathematics, a bialgebra over a field K is a vector space over K which is both a unital associative algebra and a counital coassociative coalgebra. The algebraic and coalgebraic structures are made compatible with a few more axioms. Specifically, the comultiplication and the counit are both unital algebra homomorphisms, or equivalently, the multiplication and the unit of the algebra both are coalgebra morphisms. (These statements are equivalent since they are expressed by the same commutative diagrams.)

monoid in certain category-theoretic category

sum of multiples of four 3j symbols

consistency equation which was first introduced in the field of statistical mechanics

category whose hom sets have additional structure

finite-dimensional unital associative algebra with a compatible bilinear form

category of sets and relations

monoidal category where A ⊗ B is naturally equivalent to B ⊗ A