= Functor represented by a scheme
{title2=$h_X(R)=\operatorname{Hom}(\operatorname{Spec}R,X)$}
{wiki}
= Functor of points of a scheme
{synonym}
= Functor of points
{synonym}
The functor of points describes a <scheme> through its morphisms from test <schemes>. On <commutative rings>, it is covariant because a <ring homomorphism> reverses the corresponding affine-scheme map. A functor on <rings> is represented by $X$ in the algebraic-geometric sense when it is naturally isomorphic to $h_X$. The representing <scheme> need not be affine; this is different from demanding a <representable functor> in the category of <rings> itself.
// Target: module-theory.bigb
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