# Definition

The target object, or simply target, of a morphism $f:x\to y$ in some category $C$ is the object $y$. The target of $f$ is also called its codomain, since the dual concept (the source) is also called ‘domain’.

Given a small category $C$ with set of objects ${C}_{0}$ and set of morphisms ${C}_{1}$, the target function of $C$ is the function $t:{C}_{1}\to {C}_{0}$ that maps each morphism in ${C}_{1}$ to its target object in ${C}_{0}$.

Generalising this, given an internal category $C$ with object of objects ${C}_{0}$ and object of morphisms ${C}_{1}$, the target morphism of $C$ is the morphism $t:{C}_{1}\to {C}_{0}$ that is part of the definition of internal category.