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In defining sheaf cohomology (say in Hartshorne), a common approach seems to be defining the cohomology functors as derived functors. Is there any conceptual reason for injective resolution to come ...

Apologies for the vagueness of question. Background this thread has some nice examples of presheaves failing to be sheaves. Question Is there a generic way to measure "how badly" a presheaf fails ...

Let $X$ be a topological space and $U$ an open cover of $X$. In this thread Angelo explained beautifully how presheaf cohomology (Cech cohomology) relates to sheaf cohomology: The zeroth Cech ...