On Categorical Notions of Compact Objects

Maria Manuel Clementino
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Maria Manuel Clementino: Universidade de Coimbra, Departamento de Matemática

A chapter in Categorical Topology, 1996, pp 15-29 from Springer

Abstract: Abstract Due to the nature of compactness, there are several interesting ways of defining compact objects in a category. In this paper we introduce and study an internal notion of compact objects relative to a closure operator (following the Borel-Lebesgue definition of compact spaces) and a notion of compact objects with respect to a class of morphisms (following Áhn and Wiegandt [2]). Although these concepts seem very different in essence, we show that, in convenient settings, compactness with respect to a class of morphisms can be viewed as Borel-Lebesgue compactness for a suitable closure operator. Finally, we use the results obtained to study compact objects relative to a class of morphisms in some special settings.

Keywords: factorization system; closure operator; 18A30; 54D30; 18B30; 54B30 (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0263-3_2

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DOI: 10.1007/978-94-009-0263-3_2

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