Categorical abstract algebraic logic:: (l, N)-algebraic systems

Algebraic systems play in the theory of algebraizability of pi-institutions the role that algebras play in the theory of algebraizable sentential logics. In this same sense, l-algebraic systems are to a pi-institution l what S-algebras are to a sentential logic S. More precisely, an (l, N)-algebraic system is the sentence functor reduct of an N'-reduced (N, N')-full model of a pi-institution l. Algebraic systems are formally introduced and their relationship with full models and with bilogical morphisms is investigated.