Publication result detail

Sizes and filtrations in accessible categories

LIEBERMAN, M.; VASEY, S.; ROSICKÝ, J.

Original Title

Sizes and filtrations in accessible categories

English Title

Sizes and filtrations in accessible categories

Type

WoS Article

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

accessible categories; internal size; cardinal arithmetic

Key words in English

accessible categories; internal size; cardinal arithmetic

Authors

LIEBERMAN, M.; VASEY, S.; ROSICKÝ, J.

RIV year

2021

Released

20.05.2020

Publisher

HEBREW UNIV MAGNES PRESS

Location

JERUSALEM

ISBN

0021-2172

Periodical

ISRAEL JOURNAL OF MATHEMATICS

Volume

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"
}