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Results tagged with sheaf-theory
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user 51164
For questions about sheaves on a topological space.
2
votes
What is the connection between direct/inverse image of set maps and direct/inverse image fun...
Here is a setting in which the question can be made more precise. Consider a continuous map $f: X \to Y$ of topological spaces which is also open. Let us denote by $O(X)$ and $O(Y)$ the posets of open …
- 9,491
14
votes
Sheaves of complexes and complexes of sheaves
If $A$ is a Grothendieck abelian category then $Sh(X,A)$ is a Grothendieck abelian category, in which case one can endow the category $C(Sh(X,A))$ of unbounded complexes in $Sh(X,A)$ with the injectiv …
- 9,491
2
votes
Commutativity between functors on sheaves of abelian groups
1) No. For example, if $A$ is non-empty and $f: X \to \ast$ is the map to the point then $j^*R^qf_*\mathbb{C} \cong H^q(X,\mathbb{C})$ while $R^q(f|_A)_*i^*\mathbb{C} \cong R^q(f|_A)_*\mathbb{C} \cong …
- 9,491