Full Subcategory

Let $\mathcal{C}$, $\mathcal{D}$ be Category with $\mathcal{C}\le \mathcal{D}$ Then $\mathcal{C}$ is a full subcategory of $\mathcal{D}$ iff
$\forall A,B:\mathcal{C}.\mathcal{C}[A,B]=\mathcal{D}[A,B]$
That is, $\mathcal{C}$ is simply a restriction of objects but not morphisms.