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@article{1390283,
author = {Lieberman, Michael and Rosický, Jiří},
article_location = {Cambridge},
article_number = {3},
doi = {http://dx.doi.org/10.1017/jsl.2016.39},
keywords = {metric abstract elementary class; accessible category; complete metric space},
language = {eng},
issn = {0022-4812},
journal = {The Journal of Symbolic Logic},
title = {Metric abstract elementary classes as accessible categories},
volume = {82},
year = {2017}
}
TY - JOUR
ID - 1390283
AU - Lieberman, Michael - Rosický, Jiří
PY - 2017
TI - Metric abstract elementary classes as accessible categories
JF - The Journal of Symbolic Logic
VL - 82
IS - 3
SP - 1022-1040
EP - 1022-1040
PB - CAMBRIDGE UNIV PRESS
SN - 00224812
KW - metric abstract elementary class
KW - accessible category
KW - complete metric space
N2 - 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.
ER -
LIEBERMAN, Michael and Jiří ROSICKÝ. Metric abstract elementary classes as accessible categories. \textit{The Journal of Symbolic Logic}. Cambridge: CAMBRIDGE UNIV PRESS, 2017, vol.~82, No~3, p.~1022-1040. ISSN~0022-4812. Available from: https://dx.doi.org/10.1017/jsl.2016.39.
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