A subcategory $\mathcal{A}$ of a category $\mathcal{C}$ is strictly full if it satisfies the following conditions:
- Fullness. The subcategory $\mathcal{A}$ is full.
- Closedness Under Isomorphisms. The class $\text{Obj}\webleft (\mathcal{A}\webright )$ is closed under isomorphisms.1
1That is, given $A\in \text{Obj}\webleft (\mathcal{A}\webright )$ and $C\in \text{Obj}\webleft (\mathcal{C}\webright )$, if $C\cong A$, then $C\in \text{Obj}\webleft (\mathcal{A}\webright )$.
