nLab unit object

Idea

In a monoidal category $(C, \otimes, I)$, the unit object (or tensor unit) $I$ is the object which plays the role of the unit for the tensor product $\otimes$, in that for any other object $a$ there are isomorphisms $a \otimes I \simeq a$ and $I \otimes a \simeq a$ (the unitors).

Dually, in a closed category there is a unit object which is such that maps out of it into an internal hom correspond to the external hom.

Related concepts

• unit of an adjunction

• unit of a monad

• monad terminology

• physical unit

• identity

• dual object, invertible object