Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsOpenImmersion.app_eq_invApp_app_of_comp_eq_aux
∀ {X Y U : AlgebraicGeometry.Scheme} (f : Y ⟶ U) (g : U ⟶ X) (fg : Y ⟶ X),
fg = CategoryTheory.CategoryStruct.comp f g →
∀ [h : AlgebraicGeometry.IsOpenImmersion g] (V : U.Opens),
(TopologicalSpace.Opens.map f.base).obj V =
(TopologicalSpace.Opens.map fg.base).obj ((AlgebraicGeometry.Scheme.Hom.opensFunctor g).obj V)- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- 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
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eqstatement and proof · cited by 1
- AlgebraicGeometry.IsOpenImmersion.lift_appstatement · cited by 0