Exponential objects in coreflective or quotient reflective subconstructs: A comparisonExponential objects in coreflective or quotient reflective subconstructs: A comparison
2000Dordrecht :Kluwer academic publ, 2000
Applied categorical structures. - Dordrecht, 1993, currens
BB Fest 96 Conference, JUL , 1996, UNIV CAPE TOWN, CAPE TOWN, SOUTH AFRICA
8():1-2, p. 247-256
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.