Grothendieck topology
... whose morphisms are open immersions. Then a presheaf on X is a contravariant functor from ... of sets, and a sheaf is a presheaf which satisfies the gluing axiom. The gluing ... C, J) is called a site. A presheaf on a category is a contravariant functor ... sheaf on a site to be a presheaf F such that for all objects X ... is a bijection. Halfway in between a presheaf and a sheaf is the notion ...
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Sheaf (mathematics)
... sets to obtain a bigger one. A presheaf is similar to a sheaf, but it ... is to introduce the concept of a presheaf, which captures the idea of associating local ... to get global information. Definition of a presheaf Suppose X is a topological space, and ... of modules over a fixed ring). A presheaf F of objects in C on the ... the open sets of X. A C-presheaf on X is then a contravariant ...
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Gluing axiom
... must satisfy, given that it is a presheaf, which is by definition a contravariant functor ... correct form of the gluing axiom: A presheaf F is a sheaf if for any ... structure. Sheafification How to turn a given presheaf P into a sheaf F? This is ... one should do, at least for a presheaf of sets. One should introduce an equivalence ...
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Čech cohomology
... for this cohomology. Let F be a presheaf. The 0-cochains on U with values ... cohomology of U with values in the presheaf F. We write $H\_\{\backslash delta\}C\; ...\; and\; let\; F\; A\; be\; the\; constant$presheaf which assigns to each nonempty open subset ... to be the Čech cohomology of this presheaf. A variant of Čech cohomology, called numerable ...
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User talk:Charles Matthews/Archive10
... ideals etc) is in general only a presheaf. Is there a "feasible" condition allowing to ... say (in favourable cases) when the factor presheaf will be a sheaf, without need of ... A. Then we have a the factor presheaf $\backslash Omega\backslash to\; F(\backslash Omega)=A(\backslash Omega\; ...$
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Function field (scheme theory)
... general it does not even give a presheaf! The well-known article of Kleiman, listed ... x . Let K X pre be the presheaf whose sections on U are localizations S ... X is the sheaf associated to the presheaf K X pre . Further issues Once K ...
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Wave front set
... t. the considered regularity (i.e. sub-presheaf of "smoother" functions). Definition Using local coordinates ... Omega\to O(\Omega) is the presheaf characterizing the regularity of the Fourier transform ...
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User talk:Yehsheng   (translated from Chinese)
... obtains in a big way.Pre- level (presheaf)Is similar with a level, but it ... link MoldCategory).CCenter object in spaceXOnPre- level (presheaf)Produces by the following data: Regarding eachXThe ...
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Talk:Čech cohomology
... wouldn't have been for a general presheaf, but something more like a constant sheaf ...
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Subfunctor
... category of sets gives a set-valued presheaf on C, that is, it associates sets ...
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