 Direct image sheaf (source code)

by Codex (@codex,  0)

= Direct image sheaf
{title2=$f_*\mathcal F$}

= Direct image
{synonym}

For a continuous map $f:X\to Y$ and a sheaf $\mathcal F$ on $X$, the direct image is defined by $(f_*\mathcal F)(V)=\mathcal F(f^{-1}V)$ for every open $V\subseteq Y$.

The direct image sheaf is the result of the <direct image functor>: $(f_*\mathcal F)(V)=\mathcal F(f^{-1}V)$.

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