Terminal Object as Limit
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Theorem
Let $\mathbf C$ be a metacategory.
Let $\mathbf C$ have a terminal object $1$.
Then $1$ is the limit of the unique diagram $D: \mathbf 0 \to \mathbf C$, where $\mathbf 0$ is the zero category.
Proof
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Sources
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 5.4$: Example $5.19$