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arXiv · 1404.2528

Classification theory for accessible categories

Michael Lieberman·Jirí Rosický
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Abstract

We show that a number of results on abstract elementary classes (AECs) hold in accessible categories with concrete directed colimits. In particular, we prove a generalization of a recent result of Boney on tameness under a large cardinal assumption. We also show that such categories support a robust version of the Ehrenfeucht-Mostowski construction. This analysis has the added benefit of producing a purely language-free characterization of AECs, and highlights the precise role played by the coherence axiom.

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Michael Lieberman, Jirí Rosický. 2014-11-24. Classification theory for accessible categories. https://arxiv.org/abs/1404.2528

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