Separability and aggregation of equivalence relations

We provide axiomatic characterizations of two natural families of rules for aggregating equivalence relations: the family of join aggregators and the family of meet aggregators. The central conditions in these characterizations are two separability axioms. Disjunctive separability, neutrality, and unanimity characterize the family of join aggregators. On the other hand, conjunctive separability and unanimity characterize the family of meet aggregators. We show another characterization of the family of meet aggregators using conjunctive separability and two Pareto axioms, Pareto⁺ and Pareto^?. If we drop Pareto^?, then conjunctive separability and Pareto⁺ characterize the family of meet aggregators along with a trivial aggregator.