POWER-OBJECTS IN MONOTOPOLOGICAL CATEGORIES

Abstract

An investigation is made of Cartesian closedness of monotopological categories A which are not necessarily c-categories. Results include: a description of the underlying sets of the power-objects in terms of the horn-sets of a certain monotopological subcategory of A; the fact that if A is Cartesian closed then it is subconcretely so; and the fact that if A is not topological and contains an initial source which is not a mono-source then A cannot be Cartesian closed. Various criteria concerning the existence of splitting objects in A are given, as well as the proofs of the exponential, distributive and other laws when A is Cartesian closed.