Sizes and filtrations in accessible categories

Autor: Sebastien Vasey, Jiří Rosický, Michael Lieberman
Rok vydání: 2020
Předmět:
Zdroj: Israel Journal of Mathematics. 238:243-278
ISSN: 1565-8511
0021-2172
DOI: 10.1007/s11856-020-2018-8
Popis: Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from [LRV19b], we examine set-theoretic problems related to internal sizes and prove several Lowenheim–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.
Databáze: OpenAIRE