Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.PartialMap.equiv_of_restrict_eq
∀ {X Y : AlgebraicGeometry.Scheme} (f g : X.PartialMap Y) {W₁ W₂ : X.Opens} {hW₁ : Dense ↑W₁} {hW₂ : Dense ↑W₂}
{hW₁' : W₁ ≤ f.domain} {hW₂' : W₂ ≤ g.domain}, f.restrict W₁ hW₁ hW₁' = g.restrict W₂ hW₂ hW₂' → f.equiv g- Cited by
- 2 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement and proof · cited by 8,199
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
- Densestatement and proof · cited by 359
- AlgebraicGeometry.Scheme.PartialMapstatement and proof · cited by 76
- AlgebraicGeometry.Scheme.PartialMap.domainstatement and proof · cited by 60
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.PartialMap.comp_equiv_of_equiv_leftproof · cited by 3
- AlgebraicGeometry.Scheme.PartialMap.comp_equiv_of_equiv_rightproof · cited by 2