0
votes
0answers
26 views

Endomorphisms of constant sheaves on connected spaces

In a paper by Deligne and Lusztig it says An endomorphism of a constant sheaf over a connected base is constant My interpretation of this statement is that given a (non-empty) connected ...
6
votes
1answer
117 views

Example where Čech and derived functor cohomologies don't agree.

I'm studying sheaf cohomology, and I've seen that Čech and derived functor cohomologies agree, at least on paracompact Hausdorff topological spaces. Is there a simple example of a topological space ...
3
votes
0answers
153 views

Adapted classes of objects and left (right) exact functors

I had a question about adapted classes of objects, I was confused by the definition and how it relates to left exact functors. Let $\mathcal{A}$ be an abelian category with enough injectives, let $F: ...
7
votes
0answers
253 views

Composition of derived functors and comparison between hypercohomology and sheaf cohomology

I had a few questions about compositions of derived functors, the comparison between hypercohomology, and sheaf cohomology and the following theorem from the Gelfand, Manin homological algebra book: ...