unit object

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 isomorphism $a \otimes I \simeq a$ 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.

Revised on February 4, 2014 02:57:15
by Urs Schreiber
(89.204.137.228)