Publication detail

CELLULAR CATEGORIES AND STABLE INDEPENDENCE

LIEBERMAN, M. VASEY, S. ROSICKÝ, J.

Original Title

CELLULAR CATEGORIES AND STABLE INDEPENDENCE

Type

journal article in Web of Science

Language

English

Original Abstract

We exhibit a bridge between the theory of cellular categories, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence. Roughly speaking, we show that the combinatorial cellular categories (those where, in a precise sense, the cellular morphisms are generated by a set) are exactly those that give rise to stable independence notions. We give two applications: on the one hand, we show that the abstract elementary classes of roots of Ext studied by Baldwin-Eklof-Trlifaj are stable and tame. On the other hand, we give a simpler proof (in a special case) that combinatorial categories are closed under 2-limits, a theorem of Makkai and Rosický.

Keywords

cellular categories; forking; stable independence; abstract elementary class; cofibrantly generated; roots of Ext

Authors

LIEBERMAN, M.; VASEY, S.; ROSICKÝ, J.

Released

18. 5. 2022

Publisher

CAMBRIDGE UNIV PRESS

Location

CAMBRIDGE

ISBN

1943-5886

Periodical

JOURNAL OF SYMBOLIC LOGIC

Year of study

18.05.2022

Number

18.05.2022

State

United States of America

Pages count

24

URL

http://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/abs/cellular-categories-and-stable-independence/CAE1BCB1D51CBDFE69996abs5429970A177

BibTex

@article{BUT181492,
  author="Michael Joseph {Lieberman} and Sebastien {Vasey} and Jiří {Rosický}",
  title="CELLULAR CATEGORIES AND STABLE INDEPENDENCE",
  journal="JOURNAL OF SYMBOLIC LOGIC",
  year="2022",
  volume="18.05.2022",
  number="18.05.2022",
  pages="24",
  doi="10.1017/jsl.2022.40",
  issn="1943-5886",
  url="http://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/abs/cellular-categories-and-stable-independence/CAE1BCB1D51CBDFE69996abs5429970A177"
}