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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso

{X Y : AlgebraicGeometry.Scheme} →
  (f : X ⟶ Y) →
    (𝒰 : Y.OpenCover) →
      (i : (CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰.affineRefinement.openCover).I₀) →
        (CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰.affineRefinement.openCover).X i ≅
          (CategoryTheory.Precoverage.ZeroHypercover.pullback₁ (AlgebraicGeometry.Scheme.Cover.pullbackHom 𝒰 f i.fst)
                (𝒰.X i.fst).affineCover).X
            i.snd

The pullback of the affine refinement is the pullback of the affine cover.

Defined in
Mathlib.AlgebraicGeometry.Cover.Open
Cited by
4 results in Mathlib
Foundations
Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map · cited by 1OpenCover.pullbackCoverAf…AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom · cited by 1OpenCover.pullbackCoverAf…AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map_assoc · cited by 0OpenCover.pullbackCoverAf…AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom_assoc · cited by 0OpenCover.pullbackCoverAf…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Iso · cited by 3963CategoryTheory.IsoAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.Iso.symm · cited by 993Iso.symmCategoryTheory.PreZeroHypercover.I₀ · cited by 763PreZeroHypercover.I₀CategoryTheory.PreZeroHypercover.X · cited by 649PreZeroHypercover.XCategoryTheory.Limits.pullback.fst · cited by 639pullback.fstCategoryTheory.Iso.trans · cited by 566Iso.transCategoryTheory.PreZeroHypercover.f · cited by 542PreZeroHypercover.fAlgebraicGeometry.IsOpenImmersion · cited by 476AlgebraicGeometry.IsOpenI…CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover · cited by 469ZeroHypercover.toPreZeroH…AlgebraicGeometry.Scheme.precoverage · cited by 336Scheme.precoverageAlgebraicGeometry.Scheme.OpenCover · cited by 207Scheme.OpenCoverOpenCover.pullbackCoverAffine…CITED BYCITES

Cites24

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Cited by4

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