📝Monoidal category

tags

§ Category Theory

Monoidal category (or tensor category) is a category $C$ with:

• a Bifunctor: $\otimes: C \times C \to C$ called a tensor product

  • associative up to a natural isomorphism

• an object $I$ (or $1$) that is both left and right identity of $\otimes$ (called unit object or identity object)

See also:

• Cartesian monoidal category—a monoidal category with categorical product and terminal object

• Cocartesian monoidal category—a monoidal category with categorical coproduct and initial object