Morphism

There is the Homomorphism, but here are other variants and subclasses:

• Isomorphism '(the application is also a bijection)'
• Endomorphism '(from a structure into itself)'
• Automorphism '(Iso + Endo)'

• Epimorphism
• Monomorphism

• Homeomorphism
• Diffeomorphism '(Preserves topological properties)'

• Comorphism '(A term sometimes used in Category theory)'