Abstract
Abstract An adaptation of a theorem by Herrlich [5] shows that every initially structured category A can be fully embedded in a topological category AC, which is, in fact, a MacNeille completion of A. It is then shown that A is Cartesian closed if and only if AC is. Also developed is the notion of a Cartesian closed initially structured (CCIS) hull of a category. The theory of the CCIS hull is analogous to that of the Cartesian closed topological (CCT) hull. It is proved that a category has a CCT hull-if and only if it has a CCIS hull; and this allows the list of conditions equivalent to the existence of a CCT hull to be supplemented. Examples are given, drawn mainly from the various categories of binary relations.
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