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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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.)