Definition:Inclusion Relation on Subobjects

Definition
Let $\mathbf C$ be a metacategory.

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

Let $\map {\mathbf{Sub}_{\mathbf C} } C$ be the category of subobjects of $C$.

The inclusion relation $\subseteq$ on subobjects of $C$ is defined as follows:


 * $m \subseteq m'$ there exists a morphism $f: m \to m'$

Also see

 * Inclusion Relation on Subobjects is Preordering
 * Inclusion Relation on Subobjects Induced by Category of Subobjects
 * Inclusion Relation on Subobject Classes