Mathlib Map

Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.appLE.congr_simp

∀ {X Y : AlgebraicGeometry.Scheme} (f f_1 : X ⟶ Y) (e_f : f = f_1) (U : Y.Opens) (V : X.Opens)
  (e : V ≤ (TopologicalSpace.Opens.map f.base).obj U),
  AlgebraicGeometry.Scheme.Hom.appLE f U V e = AlgebraicGeometry.Scheme.Hom.appLE f_1 U V ⋯
Defined in
Mathlib.AlgebraicGeometry.Scheme
Cited by
10 results in Mathlib
Foundations
Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.Scheme.Hom.normalizationDesc_comp · cited by 5Hom.normalizationDesc_compAlgebraicGeometry.exists_appTop_π_eq_of_isLimit · cited by 2AlgebraicGeometry.exists_…AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersion · cited by 2Scheme.ker_ideal_of_isPul…AlgebraicGeometry.exists_appTop_map_eq_zero_of_isLimit · cited by 1AlgebraicGeometry.exists_…AlgebraicGeometry.Scheme.Hom.exists_isIso_morphismRestrict_toNormalization · cited by 1Hom.exists_isIso_morphism…AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_ker_glueDataObjι · cited by 0IdealSheafData.ideal_le_k…AlgebraicGeometry.Scheme.Hom.normalization.hom_ext · cited by 0normalization.hom_extAlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp · cited by 0Scheme.ideal_ker_le_ker_Γ…AlgebraicGeometry.HasAffineProperty.coprodDesc_affineAnd · cited by 0HasAffineProperty.coprodD…AlgebraicGeometry.FormallyUnramified.hom_ext · cited by 0FormallyUnramified.hom_extQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeTopCat.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…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensAlgebraicGeometry.PresheafedSpace.Hom.base · cited by 1135Hom.baseAlgebraicGeometry.PresheafedSpace.presheaf · cited by 1104PresheafedSpace.presheafAlgebraicGeometry.LocallyRingedSpace.Hom.toHom · cited by 995Hom.toHomappLE.congr_simpCITED BYCITES

Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by10

Results whose statement or proof uses this declaration.