A subcategory $\mathcal{A}$ of $\mathcal{C}$ is full if the canonical inclusion functor $\mathcal{A}\to \mathcal{C}$ is full, i.e. if, for each $A,B\in \text{Obj}\webleft (\mathcal{A}\webright )$, the inclusion
\[ \iota _{A,B}\colon \textup{Hom}_{\mathcal{A}}\webleft (A,B\webright )\hookrightarrow \textup{Hom}_{\mathcal{C}}\webleft (A,B\webright ) \]
is surjective (and thus bijective).
