The complement u c of a mono u , if exists, is uniquely determined up to isomorphism. X is analytic if u is an analytic mono. 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.