Generalized Element

A $\Gamma$-generalized element of an object $X:\mathcal{C}$ in a Category $\mathcal{C}$ is a morphism $x:{{\Gamma}\to{X}}$ from some object $\Gamma:\mathcal{C}$. Typically, we think of such a morphism as a term of type $X$ situated in an ambient context $\Gamma$.