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Consider sheaf cohomology defined by derived functor, which means use injective resolutions of sheaves to define cohomology group. Now, if Z is the constant sheaf of group of integers on unit circle S1 with its usual topology. How to computer the first cohomology group of Z on S1?

Rick Sanchez
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    One can calculate this easily enough from a fine resolution, but are you really insisting on using an injective resolution. – Angina Seng Dec 13 '17 at 08:11
  • @LordSharktheUnknown Yes. You must use injective resolution or long exact sequence. Pure algebra. – Rick Sanchez Dec 13 '17 at 08:48
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    @raisinsec if a proof using a resolution which is not by injectives would satisfy your curiousity, you may find one here. – KReiser Nov 10 '23 at 20:07

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