A strong mono is disjuctable if it has a coflat complement. Composite of analytic monos is analytic. Y be two analytic monos. X be the join of u and v. X are the coflat complements of u and v respectively.
V c be the pullback of u c and v c .
Thus z factors through u c and v c , therefore also factors through r. Thus t X can be factored through u c and t Y can be factored through v c . Therefore they are analytic monos. Consider the category of affine schemes. Suppose A is a ring.