and maps formula_156, and then showing that these data can be glued together “over” each intersection of two open affines "U" and "V" to form a scheme "Y" which we define to be formula_151. It is not hard to show that defining each formula_158 to be the map corresponding to the inclusion of formula_25 into "S"("U") as the elements of degree zero yields the necessary consistency of the formula_158, while the consistency of the formula_154 themselves follows from the quasi-coherence assumption on "S".