Talk:Constant sheaf

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mathoverflow comment

The general definition of ${\underline {S}}$ (last paragraph) is wrong. Check out this mathoverflow question.

Also I think that the example is far too long ... but this is just my opinion. -oo- (talk) 10:30, 1 May 2010 (UTC)[reply]

nine inclusions?

In the "detailed example" why are there nine inclusions, and not five? 85.250.40.219 (talk) 23:04, 14 January 2011 (UTC)[reply]

Thanks for pointing that out. It appears that when this text was originally written (back in December 2007, see this diff), the editor was counting the trivial inclusions as well (such as {p} ⊆ {p}). In July 2008, a minor rewrite introduced the term "non-trivial" without changing the number from 9 down to 5 (see this diff). I'll fix it now. RobHar (talk) 23:34, 14 January 2011 (UTC)[reply]

separated presheaf?

The text claims that F is a separated presheaf and satisfies the gluing axiom, but not a sheaf. I believe the usual definition of a "separated presheaf" is simply one which satisfies the identity axiom (if two sections of U agree on all the members of some open cover of U then they are the same), not a sheaf whose restriction maps are injective (this almost never happens!). Thus any separated presheaf which satisfies the gluing axiom is a sheaf... 2620:101:F000:700:223:6CFF:FE98:4D1 (talk) 02:57, 6 August 2013 (UTC)[reply]

This is not correct. A separated presheaf is indeed one with injective restriction maps, and yes, they do occur in practice. For example, see the construction of the sheaf associated to a presheaf in SGA 4; Grothendieck and Verdier construct a functor L from presheaves to presheaves which turns all presheaves into separated presheaves and all separated presheaves into sheaves; thus applying L twice gives the sheaf associated to a presheaf. Ozob (talk) 03:28, 6 August 2013 (UTC)[reply]

Your response is not consistent with the definition provided at Sheaf (mathematics). 2620:101:F000:700:223:6CFF:FE98:4D1 (talk) 14:31, 8 September 2013 (UTC)[reply]