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.