Definition:Equivalent Subobjects

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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 $C$.

Two subobjects $m, m'$ of $C$ are said to be equivalent if and only if:

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

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

Also see