Sheaves 4 (Construction of sheafification)

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In this video we introduce the sheafification of a presheaf and prove that we get a bijection on stalks by the induced map.
In the notation in the last lemma the bijection was already implicit, but all that you need is the diagram. So I hope you can disentangle it and see that it's indeed true.
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You didn’t use the ‘local representability condition’ in the proof that the sheafification is a sheaf because you didn’t actually show that sections glue — you just showed they glue to a function (or, as you do it, an ordered tuple of germs). It remains to show that the representability condition holds at each point in the gluing. This is easy enough (since it is indeed a *local* condition), but your proof isn’t complete without it. Just saying! 😉

xanderlewis