Topoi and categories of fuzzy sets

Abstract Let H be a completely distributive lattice and hence a Heyting algebra. Goguen's category of fuzzy sets Set(H) Eytan's logos Fuz(H) and the topos of sheaves on H, Sh(H), are interconnected by pairs of adjoint functors between them. Each of the categories has a predicate calculus. These predicate calculi are related through the functors between the categories. Change of base lattice gives rise to several functors which preserve or reflect specific kinds of statements in the predicate calculi. This paper gives details of the categories, the predicate calculi attached to them, the functors between the categories, and the preservation properties of those functors.