Publication detail

CELLULAR CATEGORIES AND STABLE INDEPENDENCE

LIEBERMAN, M. VASEY, S. ROSICKÝ, J.

English title

CELLULAR CATEGORIES AND STABLE INDEPENDENCE

Type

WoS Article

Language

en

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 in English

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

Released

2022-05-18

Publisher

CAMBRIDGE UNIV PRESS

Location

CAMBRIDGE

ISSN

1943-5886

Journal

JOURNAL OF SYMBOLIC LOGIC

Volume

18. 05. 2022

Number

18. 05. 2022

Pages count

24

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="0022-4812",
  url="http://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/abs/cellular-categories-and-stable-independence/CAE1BCB1D51CBDFE69996abs5429970A177"
}