Limits of abstract elementary classes

TL;DR

This paper explores the closure properties of the category of abstract elementary classes (AECs) under limit constructions, broadening the understanding of accessible categories and relaxing certain assumptions.

Contribution

It demonstrates that AECs and concrete functors are closed under limit-type constructions and extends this to more general accessible categories with relaxed morphism conditions.

Findings

Category of AECs is closed under limit constructions.

Broader view of closure in accessible categories.

Relaxation of morphism constraints enhances applicability.

Abstract

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.