  We show that the category of abstract elementary classes (AECs) and concrete
functors is closed under constructions of "limit type," which generalizes the
approach of Mariano, Zambrano and Villaveces away from the syntactically
oriented framework of institutions. Moreover, we provide a broader view of this
closure phenomenon, considering a variety of categories of accessible
categories with additional structure, and relaxing the assumption that the
morphisms be concrete functors.
