Morphisms

#Catagory
Morphisms and objects are constituents of a Category. Morphisms, also called maps or arrows, relate two objects called the source and the target of the morphism.

A morphism is a map between two objects in an abstract category.

  1. A general morphism is called a homomorphism
  2. A morphism f:Y->X|100 in a category is a monomorphism if, for any two morphisms u,v:Z->Y|100, fu=fv|100 implies that u=v|50
  3. A morphism f:Y->X|100 in a category is an epimorphism if, for any two morphisms u,v:X->Z|100, uf=vf|100 implies u=v|50
  4. A bijective morphism is called an isomorphism (if there is an isomorphism between two objects, then we say they are isomorphic),
  5. A surjective morphism from an object to itself is called an endomorphism, and
  6. An isomorphism between an object and itself is called an automorphism.