Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom_assoc
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (𝒰 : Y.OpenCover)
(i : (CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰.affineRefinement.openCover).I₀)
{Z : AlgebraicGeometry.Scheme} (h : 𝒰.affineRefinement.openCover.X i ⟶ Z),
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso f 𝒰 i).inv
(CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Cover.pullbackHom 𝒰.affineRefinement.openCover f i)
h) =
CategoryTheory.CategoryStruct.comp
(AlgebraicGeometry.Scheme.Cover.pullbackHom (𝒰.X i.fst).affineCover
(AlgebraicGeometry.Scheme.Cover.pullbackHom 𝒰 f i.fst) i.snd)
h- Defined in
- Mathlib.AlgebraicGeometry.Cover.Open
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
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.invstatement and proof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
- CategoryTheory.PreZeroHypercover.Xstatement and proof · cited by 649
- CategoryTheory.PreZeroHypercover.fstatement · cited by 542
- AlgebraicGeometry.IsOpenImmersionstatement · cited by 476
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
- AlgebraicGeometry.Scheme.precoveragestatement · cited by 336
- AlgebraicGeometry.Scheme.OpenCoverstatement and proof · cited by 207
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