Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (𝒰 : Y.OpenCover)
  (i : (CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰.affineRefinement.openCover).I₀),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso f 𝒰 i).inv
      ((CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰.affineRefinement.openCover).f i) =
    CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.Precoverage.ZeroHypercover.pullback₁ (AlgebraicGeometry.Scheme.Cover.pullbackHom 𝒰 f i.fst)
            (𝒰.X i.fst).affineCover).f
        i.snd)
      ((CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰).f i.fst)

Defined in: Mathlib.AlgebraicGeometry.Cover.Open
Cited by: 1 results in Mathlib
Foundations: Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound

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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.Iso.homproof · cited by 7,684
CategoryTheory.Iso.invstatement and proof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.CategoryStruct.idproof · cited by 6,235
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CategoryTheory.Limits.pullbackproof · cited by 864
CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
CategoryTheory.PreZeroHypercover.Xstatement and proof · cited by 649
CategoryTheory.Limits.pullback.fstproof · cited by 639
CategoryTheory.Limits.pullback.sndproof · cited by 637

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AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map_assocproof · cited by 0