Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationDesc_assoc
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [inst : AlgebraicGeometry.QuasiCompact f]
[inst_1 : AlgebraicGeometry.QuasiSeparated f] {T : AlgebraicGeometry.Scheme} (f₁ : X ⟶ T) (f₂ : T ⟶ Y)
[inst_2 : AlgebraicGeometry.IsIntegralHom f₂] (H : f = CategoryTheory.CategoryStruct.comp f₁ f₂)
{Z : AlgebraicGeometry.Scheme} (h : T ⟶ Z),
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.toNormalization f)
(CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.normalizationDesc f f₁ f₂ H) h) =
CategoryTheory.CategoryStruct.comp f₁ h- Defined in
- Mathlib.AlgebraicGeometry.Normalization
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.QuasiCompactstatement and proof · cited by 102
- AlgebraicGeometry.QuasiSeparatedstatement and proof · cited by 52
- AlgebraicGeometry.Scheme.Hom.normalizationstatement · cited by 41
- AlgebraicGeometry.Scheme.Hom.toNormalizationstatement and proof · cited by 28
- AlgebraicGeometry.IsIntegralHomstatement and proof · cited by 18
- AlgebraicGeometry.Scheme.Hom.normalizationDescstatement and proof · cited by 10
- AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationDescproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.