Metric abstract elementary classes as accessible categories
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | The Journal of Symbolic Logic |
| MU Faculty or unit | |
| 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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