Theorems · Definition · algebraic geometry
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme
A morphism of Schemes is an open immersion if it is an open immersion as a morphism of LocallyRingedSpaces
- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 476 results in Mathlib
- Foundations
- Depth 99 from the axioms, rests on 1,350 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement · cited by 2,179
- AlgebraicGeometry.Scheme.Hom.toLRSHomproof · cited by 58
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersionproof · cited by 28
Cited by592
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.OpenCoverproof · cited by 207
- AlgebraicGeometry.Scheme.Hom.opensFunctorstatement and proof · cited by 204
- AlgebraicGeometry.Scheme.Hom.opensRangestatement and proof · cited by 113
- AlgebraicGeometry.Scheme.Hom.appIsostatement and proof · cited by 48
- AlgebraicGeometry.Scheme.Hom.preimage_image_eqstatement and proof · cited by 37
- AlgebraicGeometry.Scheme.Hom.isOpenEmbeddingstatement and proof · cited by 35
- AlgebraicGeometry.Scheme.Pullback.vstatement · cited by 34
- AlgebraicGeometry.Scheme.zariskiTopologyproof · cited by 34
- AlgebraicGeometry.Scheme.Hom.isoImagestatement and proof · cited by 32
- AlgebraicGeometry.Scheme.Pullback.gluingstatement · cited by 30
- AlgebraicGeometry.Scheme.Cover.ColimitGluingDatastatement · cited by 26
- AlgebraicGeometry.Scheme.Hom.image_monostatement and proof · cited by 24
Showing the 200 most cited of 592.