Polymorphisms between two predicates over larger alphabets

Extend the impossibility-domain and triviality classifications for polymorphisms from a predicate P over finite product domains to a predicate Q over finite product domains, including the case of larger alphabets, where coordinate functions map inputs from the domains of P to the corresponding domains of Q.

Background

The paper introduces a two-predicate setting in which coordinate functions map inputs satisfying a predicate P to outputs satisfying a predicate Q. This framework appears in universal algebra, social choice theory, and complexity theory.

For the special case in which the coordinate domains coincide and P is contained in Q, prior work studied a social-choice variant over the Boolean domain. The authors explicitly leave open the extension of those results to their setting and to larger alphabets.