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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.morphismRestrict_comp

∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) (U : TopologicalSpace.Opens ↥Z),
  CategoryTheory.CategoryStruct.comp f g ∣_ U =
    CategoryTheory.CategoryStruct.comp (f ∣_ (TopologicalSpace.Opens.map g.base).obj U) (g ∣_ U)
Defined in
Mathlib.AlgebraicGeometry.Restrict
Cited by
8 results in Mathlib
Foundations
Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

AlgebraicGeometry.HasRingHomProperty.of_comp · cited by 3HasRingHomProperty.of_compAlgebraicGeometry.Scheme.PartialMap.id_comp · cited by 1PartialMap.id_compAlgebraicGeometry.Scheme.PartialMap.comp_restrict_left · cited by 1PartialMap.comp_restrict_…AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization · cited by 1Hom.exists_mem_and_isIso_…AlgebraicGeometry.HasAffineProperty.isZariskiLocalAtSource · cited by 0HasAffineProperty.isZaris…AlgebraicGeometry.Scheme.PartialMap.comp_assoc · cited by 0PartialMap.comp_assocAlgebraicGeometry.HasRingHomProperty.stableUnderComposition · cited by 0HasRingHomProperty.stable…AlgebraicGeometry.HasAffineProperty.affineAnd_isStableUnderComposition · cited by 0HasAffineProperty.affineA…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Category.assoc · cited by 6433Category.assocTopCat.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.morphismRes…CITED BYCITES

Cites33

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Cited by8

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