nLab
unit object

Contents

Idea

In a monoidal category (C,,I)(C, \otimes, I), the unit object (or tensor unit) II is the object which plays the role of the unit for the tensor product \otimes, in that for any other object aa there are isomorphism aIaa \otimes I \simeq a and IaaI \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)