Sizes and filtrations in accessible categories

• Autoři: LIEBERMAN Michael; ROSICKÝ Jiří; VASEY Sébastien Bernard
• Rok publikování: 2020
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Israel Journal of Mathematics
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://doi.org/10.1007/s11856-020-2018-8
• Doi: https://doi.org/10.1007/s11856-020-2018-8
• Klíčová slova: internal size; presentability rank; existence spectrum; accessibility spectrum; filtrations; singular cardinal hypothesis
• Popis: 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.

Související projekty

• Injektivita a monády v algebře a topologii