WHEN ARE DIVISIBLE ABELIAN GROUPS INJECTIVE?

DOI10.1080/16073606.1981.9632250zbMath0484.18009OpenAlexW2046478733WikidataQ114098169 ScholiaQ114098169MaRDI QIDQ3943115

Bernhard Banaschewski

Publication date: 1981

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/16073606.1981.9632250

zbMATH Keywords

topos of sheavesgroup objectsdivisible abelian groupsinjective abelian groups

Mathematics Subject Classification ID

Categorical logic, topoi (03G30) Projectives and injectives (category-theoretic aspects) (18G05) Semigroup rings, multiplicative semigroups of rings (20M25) Homological and categorical methods for abelian groups (20K40) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Axiom of choice and related propositions (03E25) Categorical algebra (18E99)

Related Items (6)

Stability of abelian groups in a topos of sheaves ⋮ Injectivity and injective hulls of Abelian groups in a localic topos ⋮ Characterising complete boolean algebras in terms of pure essentialness ⋮ Algebra in a Grothendieck topos: Injectivity in quasi-equational classes ⋮ Boolean algebras in a localic topos ⋮ Abelian groups in a topos: injectives and injective effacements

Cites Work

• Generalized ``Boolean theory of universal algebras. I. Subdirect sums and normal representation theorem
• Abelian groups that are direct summands of every containing abelian group
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