Definition:Morphism

Definition
A morphism is an object $f$, together with two objects $X = \operatorname{dom}f$ and $Y = \operatorname{cod}f$ called the domain and codomain of $f$ repectively, written $f : X \to Y$ or $X \stackrel{f}{\longrightarrow} Y$.

Note that a morphism is not necessarily a function, and $X$, $Y$ need not be sets.

Therefore, the terms on this page are axioms, and do not equate with the definitions from set theory with the same names.