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Theorems · Definition · algebraic geometry

AlgebraicGeometry.specTargetImageFactorization

{X : AlgebraicGeometry.Scheme} →
  {A : CommRingCat} →
    (f : X ⟶ AlgebraicGeometry.Spec A) → X ⟶ AlgebraicGeometry.Spec (AlgebraicGeometry.specTargetImage f)

If f : X ⟶ Spec A is a morphism of schemes, then f factors via the inclusion of Spec (specTargetImage f) into X.

Defined in
Mathlib.AlgebraicGeometry.AffineScheme
Cited by
3 results in Mathlib
Foundations
Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.specTargetImageFactorization_comp · cited by 1AlgebraicGeometry.specTar…AlgebraicGeometry.specTargetImageFactorization_app_injective · cited by 0AlgebraicGeometry.specTar…AlgebraicGeometry.specTargetImageFactorization_comp_assoc · cited by 0AlgebraicGeometry.specTar…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.Spec · cited by 626AlgebraicGeometry.SpecAlgebraicGeometry.specTargetImage · cited by 4AlgebraicGeometry.specTar…AlgebraicGeometry.Scheme.Hom.liftQuotient · cited by 4Hom.liftQuotientAlgebraicGeometry.specTargetImageIdeal · cited by 1AlgebraicGeometry.specTar…AlgebraicGeometry.specTargetI…CITED BYCITES

Cites7

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Cited by3

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