full subcategory

A subcategory \(\mathcal{D}\) of a category \(\mathcal{C}\) is full, if for all objects \(A,B \in \mathrm{Ob}(\mathcal{D})\) following statement holds true:

\begin{align*} \mathrm{Hom}_{\mathcal{D}}(A, B) = \mathrm{Hom}_{\mathcal{C}}(A, B) \end{align*}