Detail publikace

Sizes and filtrations in accessible categories

LIEBERMAN, M. VASEY, S. ROSICKÝ, J.

Anglický název

Sizes and filtrations in accessible categories

Typ

článek v časopise ve Web of Science, Jimp

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.

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 anglicky

accessible categories; internal size; cardinal arithmetic

Vydáno

20.05.2020

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",
  year="2020",
  volume="238",
  number="1",
  month="May",
  pages="243--278",
  publisher="HEBREW UNIV MAGNES PRESS",
  address="JERUSALEM",
  issn="0021-2172"
}