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Injectivity and injective hulls of Abelian groups in a localic topos

Published online by Cambridge University Press:  17 April 2009

Kiran R. Bhutani
Kiran R. Bhutani
Affiliation:
The Catholic University of AmericaWashington, D.C., United States of America.
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Abstract

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We prove the analogue of the Baer Criterion for injectivity in the category AbShℒ of abelian groups in a topos of sheaves on a locale, that is, we show A is injective in AbShℒ if and only if it is injective relative to all S ↣ Zℒ where Zℒ is the group of integers in Shℒ. for a well-ordered locale we describe the injective hulls in AbShℒ in terms of injective hulls in Ab. Further we show that the global functor A → AE preserves injective hulls if and only if ℒ is a finite boolean locale. Finally We characterise injectives in AbShℒ for some special locales.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 1 , February 1988 , pp. 43 - 59
Copyright
Copyright © Australian Mathematical Society 1988

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