= Global sections geometric morphism
{title2=$\Delta:\mathbf{Set}\rightleftarrows\mathcal E:\Gamma$}
Every <Grothendieck topos> has a unique <geometric morphism> to sets, up to isomorphism. Its inverse image is $\Delta S=\coprod_{s\in S}1$ and its direct image is $\Gamma A=\operatorname{Hom}(1,A)$. A geometric inverse image out of sets must have this form because it preserves <coproducts> and the <terminal object>. A <local topos> is one for which $\Gamma$ itself is an inverse image.
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