Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsOpenImmersion.of_comp
∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) [AlgebraicGeometry.IsOpenImmersion g]
[AlgebraicGeometry.IsOpenImmersion (CategoryTheory.CategoryStruct.comp f g)], AlgebraicGeometry.IsOpenImmersion f- 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.PresheafedSpace.Hom.baseproof · cited by 1,135
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomproof · cited by 995
- AlgebraicGeometry.Scheme.Hom.toLRSHom'proof · cited by 895
- AlgebraicGeometry.IsOpenImmersionstatement and proof · cited by 476
- AlgebraicGeometry.Scheme.Hom.isOpenEmbeddingproof · cited by 35
- Topology.IsOpenEmbedding.of_compproof · cited by 3
- AlgebraicGeometry.IsOpenImmersion.of_isIso_stalkMapproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_Vproof · cited by 0
- AlgebraicGeometry.Scheme.IsLocallyDirected.fst_inv_eq_snd_invproof · cited by 0