Title
Exponential objects in coreflective or quotient reflective subconstructs: A comparison Exponential objects in coreflective or quotient reflective subconstructs: A comparison
Author
Publication type
article
Publication
Dordrecht :Kluwer academic publ ,
Subject
Mathematics
Source (journal)
Applied categorical structures. - Dordrecht, 1993, currens
Source (book)
BB Fest 96 Conference, JUL , 1996, UNIV CAPE TOWN, CAPE TOWN, SOUTH AFRICA
Volume/pages
8() :1-2 , p. 247-256
ISSN
0927-2852
ISI
000089053400014
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Abstract
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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