Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.preimage_image_eq
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [H : AlgebraicGeometry.IsOpenImmersion f] (U : X.Opens),
(TopologicalSpace.Opens.map f.base).obj ((AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj U) = U- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- SetLike.coeproof · cited by 8,199
- Set.preimageproof · cited by 4,946
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · 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 and proof · cited by 2,020
Cited by37
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.appIso_homstatement and proof · cited by 8
- AlgebraicGeometry.Scheme.Hom.appIso_hom'statement · cited by 5
- AlgebraicGeometry.isReduced_of_isOpenImmersionproof · cited by 5
- AlgebraicGeometry.Scheme.Hom.appIso_inv_app_assocstatement and proof · cited by 5
- AlgebraicGeometry.morphismRestrict_appproof · cited by 4
- AlgebraicGeometry.Scheme.Hom.image_injectiveproof · cited by 4
- AlgebraicGeometry.HasRingHomProperty.comp_of_isOpenImmersionproof · cited by 4
- AlgebraicGeometry.Scheme.image_basicOpenproof · cited by 3
- AlgebraicGeometry.IsOpenImmersion.ΓIso_invproof · cited by 2
- AlgebraicGeometry.isIntegral_of_isOpenImmersionproof · cited by 2
- AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersionproof · cited by 2
- AlgebraicGeometry.IsOpenImmersion.app_eq_invApp_app_of_comp_eq_auxproof · cited by 2