Saurez-vous trouvez de quel film est tiré ce script ?
Kate Gunzinger: 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...
Cooperman: Hold it, hold it, hold it. Thats -- thats not unique.
Kate Gunzinger: Yes, it is unique, Mr. Cooperman. Up to an element of
the image of f, all right? So weve pulled it back to a fixed B
here. Then you take beta of B, which takes you to 0 in C-prime, by
the commutivity of the diagram. Its therefore in the kernel of the
map g-prime, hence is in the image of the map f-prime, by the
exactness of the lower sequence...
Cooperman: No.
Kate Gunzinger: ...so we can pull it back...
Cooperman: No.
Kate Gunzinger: ...to an element in A-prime...
Cooperman: Its not well defined!
Kate Gunzinger: ...which it turns out is *well* defined *modulo* the
image of alpha. And thus defines the element in the co-kernel of
alpha... [draws arrow on diagram] and thats the "snake"! And on
Monday, well address ourselves to [Cooperman raises hand] the
co-homology of groups... and Mr. Coopermans next objections.