Clearly, any class of objects defines a discrete category when augmented with identity maps.

The identity map is a trivial example of an involution.

Every group is an example of a gyrogroup with gyr defined as the identity map.

The identity map on is an involution, of course.

This does not have to be necessarily the case: Consider a set consisting of just two points and the identity map which leaves each point fixed.

A separable channel can not be the identity map.

The closed subscheme of that corresponds to the identity map is called the universal family.

By convention, the identity map on the domain of f ).

To each edge joining two copies of K we associate the identity map.

Thus the only two field automorphisms of that leave the real numbers fixed are the identity map and complex conjugation.