Subcategory

Definition

A subcategory of a category $\mathcal{C}$ is any category ${\mathcal{C}}^{\prime }$ in which:

• $ob({\mathcal{C}}^{\prime })\subseteq ob(\mathcal{C})$
• ${\mathcal{C}}^{\prime }[a,b]\subseteq \mathcal{C}[a,b]\forall a,b:ob({\mathcal{C}}^{\prime })$

Remarks

Whenever hom-sets are preserved, then we say that ${\mathcal{C}}^{\prime }$ is a full subcategory of $\mathcal{C}$.