Definition:Inclusion Relation on 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 $C$.


The inclusion relation $\subseteq$ on subobjects of $C$ is defined as follows:

$m \subseteq m'$ if and only if there exists a morphism $f: m \to m'$


Also see


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