Throughout this paper we will let H denote the complete Heyting algebra ($H, vee, wedge, *$) with order reversing involution *. 0 and 1 denote the supermum and the infimum of $emptyset$, respectively. Given any set X, any element of $H^X$ is called H-fuzzy set (or, simply f.set) in X and will be denoted by small Greek letters, such as $mu, u, ho, sigma$. $H^X$ inherits a structure of H with order reversing involution in natural way, by definding $vee, wedge, *$ pointwise (sam notations of H are usual). If $f$ is a map from a set X to a set Y and $mu in H^Y$, then $f^{-1}(mu)$ is the f.set in X defined by f^{-1}(mu)(x) = mu(f(x))$. Also for $sigma in H^X, f(sigma)$ is the f.set in Y defined by $f(sigma)(y) = sup{sigma(x) : f(x) = y}$ ([4]). A preorder R on a set X is reflexive and transitive relation on X, the pair (X,R) is called preordered set. A map $f$ from a preordered set (X, R) to another one (Y,T) is said to be preorder preserving (inverting) if for $</TEX>x,y in X, xRy$ implies $f(x)T f(y) (resp. f(y)Tf(x))$. For the terminology and notation, we refer to [10, 11, 13] for category theory and [7] for H-fuzzy semitopogenous spaces.