Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Cover.hom_ext
∀ {X : AlgebraicGeometry.Scheme} (𝒰 : X.OpenCover) {Y : AlgebraicGeometry.Scheme} (f₁ f₂ : X ⟶ Y),
(∀ (x : 𝒰.I₀), CategoryTheory.CategoryStruct.comp (𝒰.f x) f₁ = CategoryTheory.CategoryStruct.comp (𝒰.f x) f₂) →
f₁ = f₂- Defined in
- Mathlib.AlgebraicGeometry.Gluing
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
- CategoryTheory.PreZeroHypercover.Xstatement · cited by 649
- CategoryTheory.PreZeroHypercover.fstatement and proof · cited by 542
- AlgebraicGeometry.IsOpenImmersionstatement · cited by 476
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
- CategoryTheory.cancel_epiproof · cited by 380
- AlgebraicGeometry.Scheme.precoveragestatement · cited by 336
- AlgebraicGeometry.Scheme.OpenCoverstatement and proof · cited by 207
- CategoryTheory.GlueData.Jproof · cited by 141
Cited by18
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Cover.ι_glueMorphismsproof · cited by 12
- AlgebraicGeometry.Scheme.Hom.toNormalization_fromNormalizationproof · cited by 6
- AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationDescproof · cited by 4
- AlgebraicGeometry.Scheme.IdealSheafData.inclusion_subschemeιproof · cited by 3
- AlgebraicGeometry.Scheme.exists_hom_comp_eq_comp_of_locallyOfFiniteTypeproof · cited by 2
- AlgebraicGeometry.Scheme.hom_ext_of_forallproof · cited by 2
- AlgebraicGeometry.Scheme.isPullback_of_openCoverproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.inclusion_compproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.inclusion_idproof · cited by 1
- AlgebraicGeometry.Proj.fromOfGlobalSections_toSpecZeroproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.toImageAux_specproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.normalization.hom_extproof · cited by 0