Abstract
Abstract Our aim in this chapter is to revisit some of the ‘topologically inspired’ classes of geometric morphisms which we introduced in Section C1.5, in the context of morphisms between localic toposes, and to investigate their properties in the more general context of morphisms between Grothendieck toposes. As in Section C2.4, we shall henceforth interpret ‘Grothendieck topos’ loosely as meaning any topos defined and bounded over a base to pos 𝒮 having a natural number object; but we shall often treat 𝒮 notationally as if it were the classical category Set of sets, relying on the reader to translate our arguments as required into the language of 𝒮-indexed categories as developed in Part B.
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