Theorems · Definition · algebraic geometry
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.opensFunctor
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X Y : AlgebraicGeometry.PresheafedSpace C} →
(f : X ⟶ Y) →
[H : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] →
CategoryTheory.Functor (TopologicalSpace.Opens ↑↑X) (TopologicalSpace.Opens ↑↑Y)The functor Opens X ⥤ Opens Y associated with an open immersion f : X ⟶ Y.
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- TopCat.carrierstatement · cited by 3,184
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.PresheafedSpacestatement and proof · cited by 260
- Topology.IsOpenEmbedding.functorproof · cited by 67
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersionstatement and proof · cited by 44
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_openproof · cited by 24
Cited by32
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invAppstatement and proof · cited by 24
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invAppstatement and proof · cited by 8
- AlgebraicGeometry.Scheme.Hom.appIso_homproof · cited by 8
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_appstatement and proof · cited by 5
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invAppstatement and proof · cited by 5
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturalitystatement and proof · cited by 5
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrictproof · cited by 5
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality_assocstatement and proof · cited by 4
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict_invAppstatement and proof · cited by 4
- AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eqstatement · cited by 3
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assocstatement and proof · cited by 3
- AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app'statement and proof · cited by 2