The Stacks project

Exercise 111.32.7. Let $X$ be a topological space. Let ${\mathcal F}$ be an abelian sheaf on $X$. Show that ${\mathcal F}$ is the quotient of a (possibly very large) direct sum of sheaves all of whose terms are of the form

\[ j_{!}(\underline{{\mathbf Z}}_ U) \]

where $U \subset X$ is open and $\underline{{\mathbf Z}}_ U$ denotes the constant sheaf with value ${\mathbf Z}$ on $U$.

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View Exercise 111.32.7 as pdf