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YCor
YCor
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Criteria for Representabilityrepresentability of a functor from Schemesschemes to Setssets

I have read in several texts that in order to show that a given functor from the category of schemes (over, say an algebraically closed field $k$) to $Sets$$\mathsf{Set}$ is representable, it suffices to check that it is representable in the subcategory of affine schemes. How is this the case? I have not been able to find a proof of this fact, and it may be rather trivial, but I do not see the connection.

Criteria for Representability of a functor from Schemes to Sets

I have read in several texts that in order to show that a given functor from the category of schemes (over, say an algebraically closed field $k$) to $Sets$ is representable, it suffices to check that it is representable in the subcategory of affine schemes. How is this the case? I have not been able to find a proof of this fact, and it may be rather trivial, but I do not see the connection.

Criteria for representability of a functor from schemes to sets

I have read in several texts that in order to show that a given functor from the category of schemes (over, say an algebraically closed field $k$) to $\mathsf{Set}$ is representable, it suffices to check that it is representable in the subcategory of affine schemes. How is this the case? I have not been able to find a proof of this fact, and it may be rather trivial, but I do not see the connection.

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Joakim Færgeman
Joakim Færgeman
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Criteria for Representability of a functor from Schemes to Sets

I have read in several texts that in order to show that a given functor from the category of schemes (over, say an algebraically closed field $k$) to $Sets$ is representable, it suffices to check that it is representable in the subcategory of affine schemes. How is this the case? I have not been able to find a proof of this fact, and it may be rather trivial, but I do not see the connection.