A morphism is a map between two objects in an abstract category.
1. A general morphism is called a homomorphism,
2. A morphism 
in a category is a monomorphism
if, for any two morphisms 
,
implies
that 
,
3. A morphism 
in a category is an epimorphism
if, for any two morphisms 
,
implies 
,
4. A morphism that has a two-sided inverse is called an isomorphism (if there is an isomorphism between two objects, then we say they are isomorphic),
5. A morphism from an object to itself is called an endomorphism, and
6. An isomorphism between an object and itself is called an automorphism.
