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Morphisms: Difference between revisions
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Created page with '* anamorphism * automorphism * bimorphism - both an epimorphism and a monomorphism * catamorphism * diffeomorphism * endomorphism * epimorphism * homomorphism * homeomorphism * h...' |
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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 | |||
Latest revision as of 18:20, 28 March 2025
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