Let \(\mathcal{C}\) be a category.
A subcategory \(\mathcal{D}\) of \(\mathcal{C}\) is a category, which consists of a nonempty subclass \(\mathrm{Ob}(\mathcal{D})\) of \(\mathrm{Ob}(\mathcal{C})\) and a nonempty subclass \(\mathrm{Hom}_{}(\mathcal{D})\) of \(\mathrm{Hom}_{}(\mathcal{C})\)