Definition:Subobject

Definition

Let $\mathbf C$ be a metacategory.

Let $C$ be an object of $\mathbf C$.

A subobject of $C$ is a monomorphism $m: B \rightarrowtail C$ with codomain $C$.

Also see

• Category of Subobjects
• Subobject Class
• Results about subobjects can be found here.

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (next): $\S 5.1$: Definition $5.1$