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
- Inclusion Relation on Subobjects is Preordering
- Inclusion Relation on Subobjects Induced by Category of Subobjects
- Inclusion Relation on Subobject Classes
Sources
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 5.1$