Mathlib Map

Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Cover.pullbackHom_map

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [inst : P.IsStableUnderBaseChange]
  [inst_1 : AlgebraicGeometry.Scheme.IsJointlySurjectivePreserving P] {X W : AlgebraicGeometry.Scheme}
  (𝒰 : AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X) (f : W ⟶ X)
  [inst_2 : ∀ (x : 𝒰.I₀), CategoryTheory.Limits.HasPullback f (𝒰.f x)] (i : 𝒰.toPreZeroHypercover.1),
  CategoryTheory.CategoryStruct.comp (𝒰.pullbackHom f i) (𝒰.f i) =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰).f i) f
Defined in
Mathlib.AlgebraicGeometry.Cover.MorphismProperty
Cited by
5 results in Mathlib
Foundations
Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlgebraicGeometry.Scheme.IsJointlySurjectivePreservingCategoryTheory.Limits.HasPullback
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.Scheme.Hom.support_ker · cited by 6Hom.support_kerAlgebraicGeometry.Scheme.Cover.pullbackHom_map_assoc · cited by 2Cover.pullbackHom_map_ass…AlgebraicGeometry.Scheme.Hom.isLocallyConstructible_image · cited by 1Hom.isLocallyConstructibl…AlgebraicGeometry.SurjectiveOnStalks.isEmbedding_pullback · cited by 0SurjectiveOnStalks.isEmbe…AlgebraicGeometry.IsZariskiLocalAtSource.isZariskiLocalAtTarget · cited by 0IsZariskiLocalAtSource.is…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.PreZeroHypercover.I₀ · cited by 763PreZeroHypercover.I₀CategoryTheory.PreZeroHypercover.X · cited by 649PreZeroHypercover.XCategoryTheory.PreZeroHypercover.f · cited by 542PreZeroHypercover.fCategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover · cited by 469ZeroHypercover.toPreZeroH…CategoryTheory.Limits.HasPullback · cited by 434Limits.HasPullbackAlgebraicGeometry.Scheme.precoverage · cited by 336Scheme.precoverageCategoryTheory.MorphismProperty.IsStableUnderBaseChange · cited by 131MorphismProperty.IsStable…CategoryTheory.Limits.pullback.condition · cited by 122pullback.conditionAlgebraicGeometry.Scheme.Cover · cited by 88Scheme.CoverCategoryTheory.Precoverage.ZeroHypercover.pullback₁ · cited by 64ZeroHypercover.pullback₁AlgebraicGeometry.Scheme.Cover.pullbackHom · cited by 32Cover.pullbackHomCover.pullbackHom_mapCITED BYCITES

Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.