But the semantic classes of displays frequently are subcategories, and in practice it is convenient and harmless to make this assumption. In particular it need not be the M -class for a factorisation system. Next we consider the extreme cases between which display structures interpolate. Let C be a category with specified terminal object 1 and specified binary products. D xX D , forms a display structure.
G serve as the choice of pullback.
Let C be a category with a class of displays. The presence or absence of equality types influences the quantifiers. All instances of the order relation in a meet-semilattice. If we think of subobjects as subsets with canonical inclusions then these provide a corresponding display structure . The pullback in this case is called inverse image.