Let me just show you how to *construct* the map S, which is the fun of the lemma anyhow, okay? So you assume you have an element in the kernel of gamma, that is, an element in C, such that gamma takes you to 0 in C-prime. You pull it back to B, via map g, which is surjective...
Hold it, hold it, hold it. That's -- that's not unique.
Yes, it is unique, Mr. Cooperman. Up to an element of the image of f, all right? So we've pulled it back to a fixed B here. Then you take beta of B, ...