Publication detail

Sizes and filtrations in accessible categories

LIEBERMAN, M. VASEY, S. ROSICKÝ, J.

Original Title

Sizes and filtrations in accessible categories

Type

journal article in Web of Science

Language

English

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.

Keywords

accessible categories; internal size; cardinal arithmetic

Authors

LIEBERMAN, M.; VASEY, S.; ROSICKÝ, J.

Released

20. 5. 2020

Publisher

HEBREW UNIV MAGNES PRESS

Location

JERUSALEM

ISBN

0021-2172

Periodical

ISRAEL JOURNAL OF MATHEMATICS

Year of study

238

Number

1

State

State of Israel

Pages from

243

Pages to

278

Pages count

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"
}