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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.

Defined in
Mathlib.Geometry.RingedSpace.OpenImmersion
Cited by
30 results in Mathlib
Foundations
Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersion

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp · cited by 24IsOpenImmersion.invAppAlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp · cited by 8IsOpenImmersion.app_invAppAlgebraicGeometry.Scheme.Hom.appIso_hom · cited by 8Hom.appIso_homAlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app · cited by 5IsOpenImmersion.invApp_appAlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invApp · cited by 5IsOpenImmersion.inv_invAppAlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality · cited by 5IsOpenImmersion.inv_natur…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict · cited by 5IsOpenImmersion.isoRestri…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality_assoc · cited by 4IsOpenImmersion.inv_natur…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict_invApp · cited by 4IsOpenImmersion.ofRestric…AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq · cited by 3GlueData.ι_image_preimage…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc · cited by 3IsOpenImmersion.app_invAp…AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app' · cited by 2GlueData.snd_invApp_t_app'AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app'_assoc · cited by 2IsOpenImmersion.app_inv_a…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.to_iso · cited by 2IsOpenImmersion.to_isoAlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app' · cited by 2GlueData.opensImagePreima…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorTopCat.carrier · cited by 3184TopCat.carrierTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.PresheafedSpace · cited by 260AlgebraicGeometry.Preshea…Topology.IsOpenEmbedding.functor · cited by 67IsOpenEmbedding.functorAlgebraicGeometry.PresheafedSpace.IsOpenImmersion · cited by 44PresheafedSpace.IsOpenImm…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_open · cited by 24IsOpenImmersion.base_openIsOpenImmersion.opensFunctorCITED BYCITES

Cites10

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Cited by32

Results whose statement or proof uses this declaration.