Abstract elementary classes and accessible categories
Tibor Beke, Jiri Rosicky
TL;DR
This paper compares two mathematical frameworks, abstract elementary classes and accessible categories, to understand their similarities and differences in the context of category theory and model theory.
Contribution
It provides a detailed comparison between Shelah's abstract elementary classes and accessible categories with directed colimits, highlighting their relationships.
Findings
Identifies conditions under which these frameworks coincide.
Clarifies the structural properties shared by both frameworks.
Provides insights into the categorical nature of model-theoretic classes.
Abstract
We compare abstract elementary classes of Shelah with accessible categories having directed colimits.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Rings, Modules, and Algebras