Categorical Abstract Algebraic Logic: Compatibility Operators And Correspondence Theorems

Very recently Albuquerque, Font and Jansana, based on preceding work of Czelakowski on compatibility operators, introduced coherent compatibility operators and used Galois connections, formed by these operators, to provide a unified framework for the study of the Leibniz, the Suszko and the Tarski operators of abstract algebraic logic. Based on this work, we present a unified treatment of the operator approach to the categorical abstract algebraic logic hierarchy of pi-institutions. This approach encompasses previous work by the author in this area, started under Don Pigozzi's guidance, and provides resources for new results on the semantic, i.e., operator-based, side of the hierarchy.