(mathematics, category theory) (formally) An arrow in a category; (less formally) an abstraction that generalises a map from one mathematical object to another and is structure-preserving in a way that depends on the branch of mathematics from which it arises.

plural of morphism

the state of having a specified shape or form

(category theory) hom-set

(category theory) A morphism which yields the same morphism when pre-composed with either one of a parallel pair of morphisms.

(category theory) A morphism which is both a constant morphism and a coconstant morphism.

(category theory) A morphism which yields the same morphism when post-composed with either one of a parallel pair of morphisms.

plural of zero morphism

(category theory) A morphism from an object to the product of that object with itself, which morphism is induced by a pair of identity morphisms of the said object.

(category theory) A unique morphism corresponding to each object of a category, which has its domain equal to its codomain, and which composed with any morphism (with which it is composable) gives that same morphism.