Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.comp_apply
∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) (x : ↥X),
(CategoryTheory.CategoryStruct.comp f g) x = g (f x)- Defined in
- Mathlib.AlgebraicGeometry.Scheme
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- TopCatstatement · cited by 1,889
Cited by32
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.finrank_pullback_sndproof · cited by 6
- AlgebraicGeometry.Scheme.Pullback.range_mapproof · cited by 3
- AlgebraicGeometry.spread_out_of_isGermInjective'proof · cited by 3
- AlgebraicGeometry.IsAffineOpen.fromSpec_primeIdealOfproof · cited by 3
- AlgebraicGeometry.universallyInjective_eq_diagonalproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberproof · cited by 2
- AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec_fromSpecStalkproof · cited by 2
- AlgebraicGeometry.Scheme.Pullback.Triplet.fst_SpecTensorTo_applyproof · cited by 2
- AlgebraicGeometry.exists_smooth_of_formallySmooth_stalkproof · cited by 2
- AlgebraicGeometry.Proj.fromOfGlobalSections_preimage_basicOpenproof · cited by 2
- AlgebraicGeometry.Scheme.Pullback.Triplet.snd_SpecTensorTo_applyproof · cited by 2