Definition:Category of Subobjects

Definition
Let $\mathbf C$ be a metacategory.

Let $C$ be an object of $\mathbf C$.

The category of subobjects of $C$, denoted $\mathbf{Sub}_{\mathbf C} \left({C}\right)$, is defined as follows:

The behaviour of the morphisms is shown in the following commutative diagram in $\mathbf C$:


 * $\begin{xy}\xymatrix@+1em{

B \ar[r]^*+{f} \ar[rd]_*+{m} & B' \ar[d]^*+{m'}

\\ & C }\end{xy}$

Also see

 * Category of Subobjects is Category
 * Category of Subobject Classes