Theorems · Theorem · algebraic geometry
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_open
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {X Y : AlgebraicGeometry.PresheafedSpace C} {f : X ⟶ Y}
[self : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f],
Topology.IsOpenEmbedding ⇑(CategoryTheory.ConcreteCategory.hom f.base)the underlying continuous map of underlying spaces from the source to an open subset of the target.
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 87 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.coestatement · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- TopCatstatement · cited by 1,889
- AlgebraicGeometry.PresheafedSpace.Hom.basestatement · cited by 1,135
- AlgebraicGeometry.PresheafedSpacestatement and proof · cited by 260
- Topology.IsOpenEmbeddingstatement · cited by 231
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersionstatement and proof · cited by 44
Cited by29
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.isOpenEmbeddingproof · cited by 35
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.opensFunctorproof · cited by 30
- AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrictstatement · cited by 5
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrictstatement and proof · cited by 5
- AlgebraicGeometry.IsOpenImmersion.iff_isIso_stalkMapproof · cited by 4
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrictstatement · cited by 4
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrictstatement and proof · cited by 3
- AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app'proof · cited by 2
- AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrictstatement · cited by 2
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrictstatement · cited by 2
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.to_isoproof · cited by 2
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrictstatement and proof · cited by 2