Section functor with support
= Section functor with support
{title2=$\Gamma_Z(X,-)$}
For a closed subset $Z\subseteq X$, the section functor with support is
$$
\Gamma_Z(X,\mathcal F)
=\{s\in\Gamma(X,\mathcal F):\operatorname{Supp}s\subseteq Z\}.
$$
It is left exact.