Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.comp_appTop

∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ Z),
  AlgebraicGeometry.Scheme.Hom.appTop (CategoryTheory.CategoryStruct.comp f g) =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.appTop g) (AlgebraicGeometry.Scheme.Hom.appTop f)

Defined in: Mathlib.AlgebraicGeometry.Scheme
Cited by: 7 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

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

Cites16

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

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
Top.topstatement · cited by 9,680
Oppositestatement · cited by 8,081
TopCat.carrierstatement · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333
TopologicalSpace.Opensstatement · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892

Cited by7

Results whose statement or proof uses this declaration.

AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpecproof · cited by 8
AlgebraicGeometry.IsAffineOpen.isoSpec_inv_appTopproof · cited by 3
RingHom.IsStableUnderBaseChange.pullback_fst_appTopproof · cited by 2
AlgebraicGeometry.HasRingHomProperty.of_source_openCoverproof · cited by 2
AlgebraicGeometry.Scheme.exists_isQuasiAffine_of_isLimitproof · cited by 1
AlgebraicGeometry.IsSeparated.valuativeCriterionproof · cited by 1
AlgebraicGeometry.Scheme.Hom.comp_appTop_assocproof · cited by 0