Definition:Inclusion Relation on Subobject Classes

Definition
Let $\mathbf C$ be a metacategory.

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

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


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

Also see

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