Publication detail

Sizes and filtrations in accessible categories

LIEBERMAN, M. VASEY, S. ROSICKÝ, J.

English title

Sizes and filtrations in accessible categories

Type

journal article in Web of Science

Language

en

Original abstract

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.

English abstract

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.

Keywords in English

accessible categories; internal size; cardinal arithmetic

Released

20.05.2020

Publisher

HEBREW UNIV MAGNES PRESS

Location

JERUSALEM

ISSN

0021-2172

Volume

238

Number

1

Pages from–to

243–278

Pages count

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"
}