= Affine-target adjunction for schemes
{title2=$\operatorname{Hom}(X,\operatorname{Spec}A)\simeq\operatorname{Hom}(A,\Gamma(X,\mathcal O_X))$}
A <morphism of schemes> into an <affine scheme> is uniquely determined by its homomorphism on <global sections>. Conversely, a <ring homomorphism> $A\to\Gamma(X,\mathcal O_X)$ restricts on every <affine open subscheme> of $X$ to a map into $\operatorname{Spec}A$; equality on affine covers of overlaps glues these maps. No quasi-compactness or affineness assumption on $X$ is needed.
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