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1.If we identify two schemes X $X$ and Y $Y$ as two presheaves of set on category of affine schemes.($Aff$=$Alg^{op}$schemes.($Aff:=\text{CRing}^{op}$) If there is a morphism as natural transformations f:$X--->Y$$f:X\to Y$, then, how to give the definition of the affine morphism?

2.If we identify two schemes X $X$ and Y $Y$ as two category of quasi coherent sheaves $Qcoh_{X}$ QCoh_{X}$and$Qcoh_{Y}$. QCoh_{Y}$. Then morphism between this two schemes is a functor $f$: $Qcoh_{X}-->Qcoh_{Y}$, f: Qcoh_{X}\to Qcoh_{Y}$, how to give the definition of affine morpshim ? 3.If we just consider the classical case. X and Y are two schemes. suppose$f$:$X--->Y$f:X\to Y$ is an affine morphism. Does this definition of affineness coincide with the other two definitions(if there exists)?

If such definitions of affine morphisms exists, are they equivalent or not?

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# Affine morphisms in different settings coincide?

1.If we identify two schemes X and Y as two presheaves of set on category of affine schemes.($Aff$=$Alg^{op}$) If there is a morphism as natural transformations f:$X--->Y$, then, how to give the definition of the affine morphism?

2.If we identify two schemes X and Y as two category of quasi coherent sheaves $Qcoh_{X}$ and $Qcoh_{Y}$. Then morphism between this two schemes is a functor $f$: $Qcoh_{X}-->Qcoh_{Y}$, how to give the definition of affine morpshim ?

3.If we just consider the classical case. X and Y are two schemes. suppose $f$:$X--->Y$ is an affine morphism. Does this definition of affineness coincide with the other two definitions(if there exists)?

If such definitions of affine morphisms exists, are they equivalent or not?