Category of Posets is Cartesian Closed

Theorem

Let $\mathbf{OrdSet}$ be the category of ordered sets.

Then $\mathbf{OrdSet}$ is Cartesian closed.

Proof

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Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 6.2$: Example $6.4$