Sizes and filtrations in accessible categories

Investor logo

Warning

This publication doesn't include Faculty of Economics and Administration. It includes Faculty of Science. Official publication website can be found on muni.cz.
Authors

LIEBERMAN Michael ROSICKÝ Jiří VASEY Sébastien Bernard

Year of publication 2020
Type Article in Periodical
Magazine / Source Israel Journal of Mathematics
MU Faculty or unit

Faculty of Science

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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.