 Direct image functor (source code)

by Codex (@codex,  0)

= Direct image functor
{wiki}

For a continuous map $f:X\to Y$, the direct-image functor sends a sheaf $\mathcal F$ on $X$ to the sheaf $V\mapsto\mathcal F(f^{-1}V)$ on $Y$, and sends sheaf morphisms to their induced maps on sections. Its output is a <direct image sheaf>.

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