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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.map_appLE

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {U U' : Y.Opens} {V : X.Opens}
  (e : V ≤ (TopologicalSpace.Opens.map f.base).obj U) (i : Opposite.op U' ⟶ Opposite.op U),
  CategoryTheory.CategoryStruct.comp (Y.presheaf.map i) (AlgebraicGeometry.Scheme.Hom.appLE f U V e) =
    AlgebraicGeometry.Scheme.Hom.appLE f U' V ⋯
Defined in
Mathlib.AlgebraicGeometry.Scheme
Cited by
24 results in Mathlib
Foundations
Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpec · cited by 8IsAffineOpen.SpecMap_appL…AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturality · cited by 4Opens.toSpecΓ_naturalityAlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv · cited by 4IsOpenImmersion.map_ΓIso_…AlgebraicGeometry.Proj.awayι_comp_map · cited by 3Proj.awayι_comp_mapAlgebraicGeometry.exists_appTop_π_eq_of_isLimit · cited by 2AlgebraicGeometry.exists_…AlgebraicGeometry.exists_app_map_eq_zero_of_isLimit · cited by 2AlgebraicGeometry.exists_…AlgebraicGeometry.IsOpenImmersion.ΓIso_inv · cited by 2IsOpenImmersion.ΓIso_invAlgebraicGeometry.mono_pushoutSection_of_iSup_eq · cited by 2AlgebraicGeometry.mono_pu…AlgebraicGeometry.Scheme.Hom.map_appLE_assoc · cited by 2Hom.map_appLE_assocAlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersion · cited by 2Scheme.ker_ideal_of_isPul…AlgebraicGeometry.isIso_pushoutSection_of_iSup_eq · cited by 2AlgebraicGeometry.isIso_p…AlgebraicGeometry.IsAffineOpen.appLE_eq_away_map · cited by 2IsAffineOpen.appLE_eq_awa…AlgebraicGeometry.exists_appTop_map_eq_zero_of_isLimit · cited by 1AlgebraicGeometry.exists_…AlgebraicGeometry.Scheme.isPullback_toSpecΓ_toSpecΓ · cited by 1Scheme.isPullback_toSpecΓ…AlgebraicGeometry.Scheme.Hom.coequifibered_normalizationDiagramMap · cited by 1Hom.coequifibered_normali…Quiver.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 8081OppositeTopCat.carrier · cited by 3184TopCat.carrierLE.le.trans · cited by 3151le.transAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatOpposite.unop · cited by 2231Opposite.unopTopologicalSpace.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.map_appLECITED BYCITES

Cites29

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Cited by24

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