Definition:Equivalent Subobjects

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 $C$.

Two subobjects $m, m'$ of $C$ are said to be equivalent iff:


 * $m \subseteq m'$ and $m' \subseteq m$

where $\subseteq$ denotes the inclusion relation on subobjects.

Also see

 * Equivalence of Subobjects is Equivalence