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For questions about sheaves on a topological space.

105 votes
Accepted

How should one think about sheafification and the difference between a sheaf and a presheaf

There are two ways a presheaf can fail to be a sheaf. It has local sections that should patch together to give a global section, but don't, It has non-zero sections which are locally zero. When di …
Greg Muller's user avatar
34 votes
Accepted

What is sheaf cohomology intuitively?

One way to think about $H^1(A)$ is to use the long exact sequence not as a property of cohomology, but outright as a definition. That is, given an exact sequence of sheaves, $$ 0\rightarrow A\rightar …
Greg Muller's user avatar