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I rewrote a good bit of the entry sheaf, trying to polish and strengthen the exposition.
The rewritten material is what now constituttes the section “Definition”. This subsumes essentially everything that was there before, except for some scattered remarks which I removed and instad provided hyperlinks for, since they have meanwhile better discussions in other entries.
I left the discussion of sheaves and the general notion of localization untouched (it is now in the section “Sheaves” and localization”). This would now need to be harmonized notationally a bit better. Maybe later.
I’ve been using SheaF as a quirky editor name, but I realize now its been cumulating at ’Pages contributed to’. Sorry about that, I’ll cut that out.
Definition 2.6 seems wrong to me unless I am misreading it. It claims that a presheaf is a sheaf when, for each covering family , the presheaf is right orthogonal to each . That can’t be right. The correct definition involves taking the corresponding sieve and then checking that is orthogonal to that.
The preceding Remark 2.5 introduces that sieve , doesn’t it, and Def. 2.6 refers to that notion, it seems to me. (?)
(In either case, there is much room to polish this entry further.)
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