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:

$\eqclass m {} \subseteq \eqclass {m'} {}$ if and only if 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