Categorical Abstract Algebraic Logic: Closure Operators on Classes of PoFunctors

Abstract

Following work of Palasinska and Pigozzi on partially ordered varieties and quasi-varieties of universal algebras, the author recently introduced partially ordered systems (posystems) and partially ordered functors (pofunctors) to cover the case of the algebraic systems arising in categorical abstract algebraic logic. Analogs of the ordered homomorphism theorems of universal algebra were shown to hold in the context of pofunctors. In the present work, operators on classes of pofunctors are introduced and it is shown that classes of pofunctors are closed under the HSP and the SPPU operators, forming analogs of the well-known variety and quasi-variety operators, respectively, of universal algebra.