Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.opensFunctor
{X Y : AlgebraicGeometry.Scheme} →
(f : X ⟶ Y) → [H : AlgebraicGeometry.IsOpenImmersion f] → CategoryTheory.Functor X.Opens Y.OpensThe functor opens X ⥤ opens Y associated with an open immersion f : X ⟶ Y.
- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 204 results in Mathlib
- Foundations
- Depth 100 from the axioms, rests on 1,494 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.Functorstatement · cited by 16,252
- 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 · cited by 1,149
- AlgebraicGeometry.IsOpenImmersionstatement and proof · cited by 476
- AlgebraicGeometry.Scheme.Hom.toLRSHomproof · cited by 58
Cited by215
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.appIsostatement · cited by 48
- AlgebraicGeometry.Scheme.Hom.preimage_image_eqstatement · cited by 37
- AlgebraicGeometry.Scheme.Hom.isoImagestatement and proof · cited by 32
- AlgebraicGeometry.Scheme.Hom.image_monostatement · cited by 24
- AlgebraicGeometry.image_morphismRestrict_preimagestatement · cited by 20
- AlgebraicGeometry.Scheme.Hom.image_top_eq_opensRangestatement · cited by 17
- AlgebraicGeometry.Scheme.Opens.topIso_invstatement · cited by 15
- AlgebraicGeometry.Scheme.PartialMap.compproof · cited by 15
- AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_infstatement · cited by 15
- AlgebraicGeometry.Scheme.ι_image_homOfLE_le_ι_imagestatement and proof · cited by 15
- AlgebraicGeometry.Scheme.Modules.restrictAppIsostatement · cited by 14
- AlgebraicGeometry.Scheme.Opens.topIso_homstatement · cited by 10
Showing the 200 most cited of 215.