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.
Partial financial assistance by Centro de Matemática de Universidade de Comibra and by a NATO Collaborative Grant (CRG 940847) is gratefully acknowledged.
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© 1996 Kluwer Academic Publishers
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Clementino, M.M. (1996). On Categorical Notions of Compact Objects. In: Giuli, E. (eds) Categorical Topology. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0263-3_2
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DOI: https://doi.org/10.1007/978-94-009-0263-3_2
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