Morphisms: Difference between revisions
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a [https://en.wikipedia.org/wiki/Morphism morphism] is a structured, composable mapping. 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 | * anamorphism | ||
* catamorphism | * catamorphism | ||
* diffeomorphism | * diffeomorphism | ||
* endomorphism | * endomorphism: a morphism with identical source and target | ||
* epimorphism | * epimorphism | ||
* homomorphism | * homomorphism | ||
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* hylomorphism | * hylomorphism | ||
* isomorphism | * isomorphism | ||
* paramorphism | * 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 | |||