Sizes and filtrations in accessible categories
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Periodical |
| Magazine / Source | Israel Journal of Mathematics |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1007/s11856-020-2018-8 |
| Doi | http://dx.doi.org/10.1007/s11856-020-2018-8 |
| Keywords | internal size; presentability rank; existence spectrum; accessibility spectrum; filtrations; singular cardinal hypothesis |
| Description | Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. We examine set-theoretic problems related to internal sizes and prove several Löwenheim–Skolem theorems for accessible categories. For example, assuming the singular cardinal hypothesis, we show that a large accessible category has an object in all internal sizes of high enough co-finality. We also prove that accessible categories with directed colimits have filtrations: any object of sufficiently high internal size is (the retract of) a colimit of a chain of strictly smaller objects. |
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