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AlgebraicGeometry.Scheme.Hom.congr_app

∀ {X Y : AlgebraicGeometry.Scheme} {f g : X ⟶ Y} (e : f = g) (U : Y.Opens),
  AlgebraicGeometry.Scheme.Hom.app f U =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.app g U)
      (X.presheaf.map (CategoryTheory.eqToHom ⋯).op)
Defined in
Mathlib.AlgebraicGeometry.Scheme
Cited by
9 results in Mathlib
Foundations
Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
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AlgebraicGeometry.Scheme.homOfLE_app · cited by 7Scheme.homOfLE_appAlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app · cited by 5IdealSheafData.subschemeι…AlgebraicGeometry.morphismRestrict_app · cited by 4AlgebraicGeometry.morphis…AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage · cited by 2Hom.toNormalization_app_p…AlgebraicGeometry.liftCoborder_app · cited by 1AlgebraicGeometry.liftCob…AlgebraicGeometry.Scheme.Hom.toImage_app · cited by 1Hom.toImage_appAlgebraicGeometry.Scheme.Hom.inv_app · cited by 1Hom.inv_appAlgebraicGeometry.Scheme.Hom.fromNormalization_app · cited by 1Hom.fromNormalization_appAlgebraicGeometry.Scheme.SpecMap_presheaf_map_eqToHom · cited by 0Scheme.SpecMap_presheaf_m…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.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatCategoryTheory.Category.comp_id · cited by 2119Category.comp_idTopologicalSpace.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…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…Hom.congr_appCITED BYCITES

Cites24

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Cited by9

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