Universal abstract elementary classes and locally multipresentable categories

Abstract

We exhibit an equivalence between the model-theoretic framework of universal classes and the category-theoretic framework of locally multipresentable categories. We similarly give an equivalence between abstract elementary classes (AECs) admitting intersections and locally polypresentable categories. We use these results to shed light on Shelah's presentation theorem for AECs.

14 pages. Some typos removed

References in corpus (2)

• Shelah's eventual categoricity conjecture in universal classes: part I
• $\mu$-Abstract Elementary Classes and other generalizations

Cited by in corpus (6)

• Forking independence from the categorical point of view
• Internal sizes in $\mu$-abstract elementary classes
• Structural Logic and Abstract Elementary Classes with Intersection
• Formal Model Theory & Higher Topology
• Hilbert spaces and $C^{\ast }$-algebras are not finitely concrete
• Unstable independence from the categorical point of view