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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 ...

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 ...