Metric abstract elementary classes as accessible categories

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Authors

LIEBERMAN Michael ROSICKÝ Jiří

Year of publication 2017
Type Article in Periodical
Magazine / Source The Journal of Symbolic Logic
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1017/jsl.2016.39
Field General mathematics
Keywords metric abstract elementary class; accessible category; complete metric space
Description We show that metric abstract elementary classes are coherent accessible categories with directed colimits, with concrete $\aleph_1$-directed colimits and concrete monomorphisms. More broadly, we define a notion of $\kappa$-concrete Abstract Elementary Class and develop the theory of such categories, beginning with a category-theoretic analogue of Shelah's Presentation Theorem and a proof of the existence of an Ehrenfeucht-Mostowski functor in case the category is large.
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