# ๐Monoidal category

*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 categoryโa monoidal category with categorical product and terminal object
- Cocartesian monoidal categoryโa monoidal category with categorical coproduct and initial object