Is the unique morphism from the empty scheme $\operatorname{Spec}((0))$ to some other scheme $X$ smooth?

Question

This is a very pedantic question, but

Is the unique morphism from the empty scheme $\emptyset = \operatorname{Spec}((0))$ to some other scheme $X$ smooth?

Answer 1

Yes. It doesn't matter which definition you choose, smoothness of $\emptyset \to X$ is satisfied for trivial reasons. More generally, any open immersion is smooth.