Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.hom_ext_of_forall
∀ {X Y : AlgebraicGeometry.Scheme} (f g : X ⟶ Y),
(∀ (x : ↥X), ∃ U, x ∈ U ∧ CategoryTheory.CategoryStruct.comp U.ι f = CategoryTheory.CategoryStruct.comp U.ι g) → f = g- Defined in
- Mathlib.AlgebraicGeometry.Gluing
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
- AlgebraicGeometry.Scheme.Opens.toSchemestatement and proof · cited by 433
- AlgebraicGeometry.Scheme.Opens.ιstatement and proof · cited by 275
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IsLocallyDirected.fst_inv_eq_snd_invproof · cited by 0
- AlgebraicGeometry.FormallyUnramified.hom_extproof · cited by 0