Spectrum of direct product is disjoint union of spectra

Verbal statement
The spectrum of a direct product of commutative unital rings is the disjoint union of their spectra (both as a set, and as a topological space).

Category-theoretic statement
The spectrum, viewed as a contravariant functor, from the category of commutative unital rings to the category of sets (resp. the category of topological spaces or the category of locally ringed spaces) converts products to coproducts.