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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invApp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : AlgebraicGeometry.PresheafedSpace C} (f : X ⟶ Y)
  [H : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] (U : TopologicalSpace.Opens ↑↑X),
  CategoryTheory.inv (AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp f U) =
    CategoryTheory.CategoryStruct.comp
      (f.c.app (Opposite.op ((AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.opensFunctor f).obj U)))
      (X.presheaf.map (CategoryTheory.eqToHom ⋯))
Defined in
Mathlib.Geometry.RingedSpace.OpenImmersion
Cited by
5 results in Mathlib
Foundations
Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersion
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.Scheme.Hom.appIso_hom · cited by 8Hom.appIso_homAlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app' · cited by 2GlueData.snd_invApp_t_app'AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app · cited by 1GlueData.f_invApp_f_appAlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_invApp · cited by 0IsOpenImmersion.inv_invAppAlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_invApp · cited by 0IsOpenImmersion.inv_invAppCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idTopCat.carrier · cited by 3184TopCat.carrierTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.PresheafedSpace.Hom.base · cited by 1135Hom.baseAlgebraicGeometry.PresheafedSpace.presheaf · cited by 1104PresheafedSpace.presheafCategoryTheory.Functor.op · cited by 997Functor.opIsOpenImmersion.inv_invAppCITED BYCITES

Cites30

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Cited by5

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