Dialectica space
Given a category "C" and a specific object "K" of "C" with certain ( logical ) properties , one can construct the category of Dialectica spaces over "C" , whose objects are pairs of objects of "C" , related by a "C"-morphism into the given object . 
<triplet> category <subj> morphism <obj> has parts of the class <triplet> morphism <subj> category <obj> part of