Definition:Subobject Class

Definition
Let $\mathbf C$ be a metacategory.

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

Let $\mathbf{Sub}_{\mathbf C} \left({C}\right)$ be the category of subobjects of $C$.

A subobject class of $C$ is an equivalence class of subobjects of $C$ under the equivalence of subobjects.

If $m$ is a subobject, its associated subobject class may be denoted by $\overline m$ or $\left[\!\left[{m}\right]\!\right]$.

Also known as
Many authors like to abuse language and call this a subobject as well.

Also see

 * Subobject
 * Category of Subobject Classes
 * Inclusion Relation on Subobject Classes