Theorems · Theorem · algebraic geometry
AlgebraicGeometry.AffineTargetMorphismProperty.diagonal_of_openCover_source
∀ {Q : AlgebraicGeometry.AffineTargetMorphismProperty} [Q.IsLocal] {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y)
(𝒰 : X.OpenCover) [inst : ∀ (i : 𝒰.I₀), AlgebraicGeometry.IsAffine (𝒰.X i)] [inst_1 : AlgebraicGeometry.IsAffine Y],
(∀ (i j : 𝒰.I₀), Q (CategoryTheory.Limits.pullback.mapDesc (𝒰.f i) (𝒰.f j) f)) → Q.diagonal f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Limits.pullbackstatement and proof · cited by 864
- CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.PreZeroHypercover.Xstatement and proof · cited by 649
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.quasiSeparatedSpace_of_isOpenCoverproof · cited by 0