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On Categorical Notions of Compact Objects

In: Categorical Topology

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  • Maria Manuel Clementino

    (Universidade de Coimbra, Departamento de Matemática)

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.

Suggested Citation

  • Maria Manuel Clementino, 1996. "On Categorical Notions of Compact Objects," Springer Books, in: Eraldo Giuli (ed.), Categorical Topology, pages 15-29, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-0263-3_2
    DOI: 10.1007/978-94-009-0263-3_2
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