Detail publikace

Sizes and filtrations in accessible categories

LIEBERMAN, M. VASEY, S. ROSICKÝ, J.

Anglický název

Sizes and filtrations in accessible categories

Typ

Článek WoS

Jazyk

en

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.

Klíčová slova anglicky

accessible categories; internal size; cardinal arithmetic

Vydáno

2020-05-20

Nakladatel

HEBREW UNIV MAGNES PRESS

Místo

JERUSALEM

ISSN

0021-2172

Ročník

238

Číslo

1

Strany od–do

243–278

Počet stran

36

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"
}