A morphismis a mapping between sets. The different types of morphism are

Every morphism send the identity in the domain to the identity in the codomain. This is easy to prove:

Ifis the identity element in the domain with operationthen

sois the identity element in the codomain.

The relationship between the different types of morphism may be written

automorphismsisomorphismsmonomorphismshomomorphisms.

Endomorphisms do not fit easiliy into this relationship since they are not isomorphisms and must be from a set into the same set.