# Masaryk University

Publication details

# Metric abstract elementary classes as accessible categories

Authors 2017 Article in Periodical The Journal of Symbolic Logic http://dx.doi.org/10.1017/jsl.2016.39 General mathematics metric abstract elementary class; accessible category; complete metric space 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.