Functor represented by a scheme

In algebraic geometry, a functor represented by a scheme X is a set-valued contravariant functor on the category of schemes such that the value of the functor at each scheme S is the set of all morphisms . The functor F is then said to be naturally equivalent to the functor of points of X; and the scheme X is said to represent the functor F, and to classify geometric objects over S given by F.

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