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| :DISC_SOFTEN-CAUS.1SG-4-see-2PL.SUBJ.PERF way-4-build-CONST NOMZ-object-to_name-4 s, DISC_SHOULD_BE_OBVIOUS-PASS-APPL_TELIC-sow-3SG.N NOMZ-PASS-examine-show-at_first-4 TAG | | :DISC_SOFTEN-CAUS.1SG-4-see-2PL.SUBJ.PERF way-4-build-CONST NOMZ-object-to_name-4 s, DISC_SHOULD_BE_OBVIOUS-PASS-APPL_TELIC-sow-3SG.N NOMZ-PASS-examine-show-at_first-4 TAG |
| :KATE: ''Let me just show you how to construct the map s, which is the fun of the lemma anyhow, okay?'' (in the diagram this map corresponds to the long curved arrow.) | | :KATE: ''Let me just show you how to construct the map s, which is the fun of the lemma anyhow, okay?'' (in the diagram this map corresponds to the long curved arrow.) |
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| DISC_SO-COND-exist-3SG.N.GNO element in kernel-CONST γ, in_order-NMLZ-say element in C, such_that 4SG-carry-3SG.N.GNO γ to 0 in C'.
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| 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’.
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| You pull it back to B, via map g, which is surjective,
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| COOPERMAN (a student): Hold it, hold it. That’s … that’s not unique.
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| KATE: Yes, it is unique, Mr. Cooperman, up to an element in the image of f, all right? So we’ve pulled it back to a fixed b here and then you take \beta of b, which takes you to 0 in C’, by the commutivity (should be commutativity) of the diagram. It is therefore in the kernel of the map g’, hence is an image of f’ by the exactness of the lower sequence…
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| :COOPERMAN: ''Werpi.''
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| :werpi
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| :I_HAVE_DOUBTS
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| :COOPERMAN: No.
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| KATE: … so we can pull it back to an element in A’…
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| COOPERMAN: It’s not well-defined.
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| KATE: …which it turns out is well-defined modulo the image of \alpha, and thus defines an element in the cokernel of \alpha, (at this point she draws the long curved arrow on the blackboard) and that’s the snake. And on Monday we’ll address ourselves to the cohomology of groups (Cooperman raises his hand) and Mr. Cooperman’s next objections.
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| [[Category:Talmic languages]] | | [[Category:Talmic languages]] |