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Let $\mathbf C$ be a metacategory.
A terminal object of $\mathbf C$ is an object $1 \in \mathbf C_0$ of $\mathbf C$ such that:
- For all $C \in \mathbf C_0$, there is a unique morphism $C \to 1$.
Also known as
A terminal object is also known as a final object.