Weakly Algebraizable π-Institutions

Weakly algebraizable sentential logics were introduced by Czelakowski and Jansana and constitute a class in the abstract algebraic hierarchy of logics lying between the protoalgebraic logics of Blok and Pigozzi and the algebraizable logics, in the sense of Czelakowski’s and Hermann’s generalization of the original notion introduced by Blok and Pigozzi. Very recently protoalgebraic π-institutions were introduced by the author in order to abstract the algebraic hierarchy to the categorical level. The present work continues this program by introducing the class of weakly algebraizable π-institutions, a proper superclass of protoalgebraic π-institutions, sharing many of the properties of the weakly algebraizable sentential logics of Czelakowski and Jansana.