Detail publikačního výsledku

Sizes and filtrations in accessible categories

LIEBERMAN, M.; VASEY, S.; ROSICKÝ, J.

Originální název

Sizes and filtrations in accessible categories

Anglický název

Sizes and filtrations in accessible categories

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

accessible categories; internal size; cardinal arithmetic

Klíčová slova v angličtině

accessible categories; internal size; cardinal arithmetic

Autoři

LIEBERMAN, M.; VASEY, S.; ROSICKÝ, J.

Rok RIV

2021

Vydáno

20.05.2020

Nakladatel

HEBREW UNIV MAGNES PRESS

Místo

JERUSALEM

ISSN

0021-2172

Periodikum

ISRAEL JOURNAL OF MATHEMATICS

Svazek

238

Číslo

1

Stát

Stát Izrael

Strany od

243

Strany do

278

Strany počet

36

URL

https://link.springer.com/article/10.1007/s11856-020-2018-8

BibTex

@article{BUT164521,
  author="Michael Joseph {Lieberman} and Sebastien {Vasey} and Jiří {Rosický}",
  title="Sizes and filtrations in accessible categories",
  journal="ISRAEL JOURNAL OF MATHEMATICS",
  year="2020",
  volume="238",
  number="1",
  pages="243--278",
  doi="10.1007/s11856-020-2018-8",
  issn="0021-2172",
  url="https://link.springer.com/article/10.1007/s11856-020-2018-8"
}