Detail publikace

CELLULAR CATEGORIES AND STABLE INDEPENDENCE

LIEBERMAN, M. VASEY, S. ROSICKÝ, J.

Anglický název

CELLULAR CATEGORIES AND STABLE INDEPENDENCE

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova anglicky

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

Vydáno

18.05.2022

Nakladatel

CAMBRIDGE UNIV PRESS

Místo

CAMBRIDGE

ISSN

1943-5886

Ročník

18.05.2022

Číslo

18.05.2022

Počet stran

24

BIBTEX


@article{BUT181492,
  author="Michael Joseph {Lieberman} and Sebastien {Vasey} and Jiří {Rosický},
  title="CELLULAR CATEGORIES AND STABLE INDEPENDENCE",
  year="2022",
  volume="18.05.2022",
  number="18.05.2022",
  month="May",
  publisher="CAMBRIDGE UNIV PRESS",
  address="CAMBRIDGE",
  issn="1943-5886"
}