Well, I am not trying to be snide, but for me, my argument is more understandable. But if you prefer to see it in the way you put it, I have no objection. A couple more comments. In 1986 (or, really, 1984), I did not really understand that this argument was *really* the same argument, just dressed up nicer, using functors instead of diagrams. In 1970, I was fresh from homological algebra. The construction struck me (and still does) as reminiscent of the argument you use in showing that if you have the beginnings of a map from a projective complex to an acyclic one, you can continue it one more step. The main difference was that this was a well-founded poset instead of an inter-indexed chain. And if anyone ever wondered why I called these A diagrams and P diagrams, it had nothing to do with A&P and everything to do with acyclic and projective. Thus the embedding theorem is, like many other things I have done, a form of acyclic models.