's proof of the "Snake Lemma" at the very beginning of the movie is technically perfect. In Charles A. Weibel's book, "An Introduction to Homological Algebra" (Cambridge U. Press, 1994), there appears the following: "We will not print the proof (of the Snake Lemma) in these notes, because it is best done visually. In fact, a clear proof is given by Jill Clayburgh at the beginning of the movie 'It's My Turn.'" See more
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, ...