(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.

(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.

(category theory) The terminal object of a comma category from a functor to a fixed object; or, dually, the initial object of a comma category from a fixed object to a functor.

(category theory) A morphism from an object to the subobject classifier which corresponds to a unique subobject of the said object, which subobject is the pullback, along this morphism, of the "true" global element of the subobject classifier.

(category theory) An isomorphism between a pair of products which have the same components but in swapped order, which isomorphism commutes with the two associated product diagrams.