nLab
identity function

Given a set SS, the identity function on SS is the function id S:SSid_S\colon S \to S that maps any element xx of SS to itself:

id S=(xx)=λx.x; id_S = (x \mapsto x) = \lambda x.\; x ;

or equivalently,

id S(x)=x. id_S(x) = x .

The identity functions are the identity morphisms in the category Set of sets.

More generally, in any concrete category, the identity morphism of each object is given by the identity function on its underlying set.

Revised on July 20, 2012 01:37:51 by Toby Bartels (75.88.84.217)