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Title
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Exponential objects in coreflective or quotient reflective subconstructs: A comparison
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Author
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Abstract
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| We prove that in the construct PRAP of pre-approach spaces the class of exponential objects completely determines the exponential objects in certain subconstructs. We show that Exp B subset of Exp PRAP for every coreflective subconstruct B and from this inclusion we deduce the equality Exp B = B boolean AND Exp PRAP for every subconstruct B that is coreflective and finitely productive. We prove that the same equality holds for non-trivial quotient reflective subconstructs. These results induce well known answers to similar questions on the construct of pretopological spaces and are compared to the topological situation. |
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Language
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English
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Source (journal)
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Applied categorical structures. - Dordrecht, 1993, currens
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Source (book)
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BB Fest 96 Conference, JUL , 1996, UNIV CAPE TOWN, CAPE TOWN, SOUTH AFRICA
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Publication
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Dordrecht
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Kluwer academic publ
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2000
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ISSN
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0927-2852
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DOI
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10.1023/A:1008674618754
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Volume/pages
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8
:1-2
, p. 247-256
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ISI
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000089053400014
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Full text (Publisher's DOI)
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