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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.appIso_hom

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [H : AlgebraicGeometry.IsOpenImmersion f] (U : X.Opens),
  (AlgebraicGeometry.Scheme.Hom.appIso f U).hom =
    CategoryTheory.CategoryStruct.comp
      (AlgebraicGeometry.Scheme.Hom.app f ((AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj U))
      (X.presheaf.map (CategoryTheory.eqToHom ⋯).op)
Defined in
Mathlib.AlgebraicGeometry.OpenImmersion
Cited by
8 results in Mathlib
Foundations
Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsOpenImmersion
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.Scheme.Hom.appIso_hom' · cited by 5Hom.appIso_hom'AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage · cited by 2Hom.toNormalization_app_p…AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst · cited by 1Scheme.coprodPresheafObjI…AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd · cited by 1Scheme.coprodPresheafObjI…AlgebraicGeometry.Scheme.Hom.appIso_homOfLE_inv · cited by 0Hom.appIso_homOfLE_invAlgebraicGeometry.Scheme.Hom.id_appIso · cited by 0Hom.id_appIsoAlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp · cited by 0Scheme.ideal_ker_le_ker_Γ…AlgebraicGeometry.Scheme.Hom.comp_appIso · cited by 0Hom.comp_appIsoQuiver.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.Iso.hom · cited by 7684Iso.homCategoryTheory.NatTrans.app · cited by 7406NatTrans.appTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…Quiver.Hom.op · cited by 1948Hom.opAlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…Hom.appIso_homCITED BYCITES

Cites33

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Cited by8

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