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- W4299649461 abstract "We show that metric abstract elementary classes (mAECs) are, in the sense of [LR] (i.e. arXiv:1404.2528), coherent accessible categories with directed colimits, with concrete $aleph_1$-directed colimits and concrete monomorphisms. More broadly, we define a notion of $kappa$-concrete AEC---an AEC-like category in which only the $kappa$-directed colimits need be concrete---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. For mAECs in particular, arguments refining those in [LR] yield a proof that any categorical mAEC is $mu$-d-stable in many cardinals below the categoricity cardinal." @default.
- W4299649461 created "2022-10-02" @default.
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- W4299649461 date "2015-04-10" @default.
- W4299649461 modified "2023-10-17" @default.
- W4299649461 title "Metric abstract elementary classes as accessible categories" @default.
- W4299649461 doi "https://doi.org/10.48550/arxiv.1504.02660" @default.
- W4299649461 hasPublicationYear "2015" @default.
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