If C1, …, Ck are members of a certain class of suitable categories (which contains those arising from models with dimension), C = C1 × … × Ck, C′ is a suitable category, F: C → C′ is a partial recursive combinatorial functor satisfying a certain property (which, if C = C1, is that F is nonconstant) and ∈ C, then (1) if F is regressive so is as is each i, and (2) if F is Dedekind then each i is Dedekind.