Definition:Equivalent Subobjects
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Definition
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
Sources
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 5.1$