Morphisms

we're using category theory definitions here, but where the term is used elsewhere, i'll try to note that.

• morphism: a structure-preserving relationship
  • operating on a source and target (often called domain and codomain)
  • with the partial binary composition operator represented by ∘
    • this operator is associative and respects identity
  • a category is made up of the class of objects (often sets) and class of morphisms (often functions).
• anamorphism
• catamorphism
• diffeomorphism
• endomorphism: a morphism with identical source and target
• epimorphism
• homomorphism
• homeomorphism
• hylomorphism
• isomorphism
• paramorphism
• monomorphism: a left-cancellative morphism
  • often called a "mono". monomorphic behavior is often called "monic".
  • in algebra, an injective homomorphism
• bimorphism: both an epimorphism and a monomorphism
• automorphism: both an endomorphism and an isomorphism