Added "Pulling back sections" section in modules.tex #184
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- Moved everything from modules.tex to sheaves.tex. After all, the results we use are from the latter chapter, so it seemed to fit better there. - Defined the inverse image section, proven its functorial properties, and made the connection with the pullback section.
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I am going to leave this pull request open because it may make sense to add a little bit about this notion, but earlier and more naively. Namely, I would say that the compatibilities shown in this commit suggest that we've already been using this notion much earlier. And in fact, the construction in Section 21 of the pullback by f of a sheaf of sets F, as the sheafification of Related: variant for sheaves on sites and pullback on cohomology. |
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Defined the pullback of a section of a sheaf of modules along a morphism of ringed spaces. Collected basic functorial properties.
I know this material may very basic, but it's nowhere treated. Despite this, the concept is extensively used in algebraic geometry and in particular in the Stacks Project:
f* : Γ_*(X,ℒ) → Γ_*(Y,f*ℒ).• The statement of Tag 08RU.
• The proof of Tag 0H79.
(The list might not be exhaustive, it's only the instances I came across so far.)