some exercises to realize the very basic concepts of the sheaves and presheaves

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I am reading my notes on sheaves and presheaves, that I wrote many years ago. But I can not get a deep connection to the subject, and when I read them, after some hours I will forget them.

I think the solution is to solve a few exercises (like 10-15 exercises to 20-30 exercises) on the subject. I am not looking for hard problems or problems for competitions. I am looking for a few informative, instructive problems on the subject. I should emphasize that I am very beginner to the subject, and I just want to deal with:

  • The definition of Sheaves and presheaves
  • Stalks
  • Morphism of sheaves
  • Sheafification
  • Some simple connection with category theory
  • Some relations with the Picard group.

For instance, I am not looking for some problems concerning Cohomology, because I do not know cohomology yet.


Can anyone introduce a good reference to find some pedagogic problems on sheaves and presheaves? something like a chapter of a book, or a note or something else.