Theorems · Theorem · commutative algebra
CommRingCat.comp_apply
∀ {R S T : CommRingCat} (f : R ⟶ S) (g : S ⟶ T) (r : ↑R),
(CategoryTheory.ConcreteCategory.hom (CategoryTheory.CategoryStruct.comp f g)) r =
(CategoryTheory.ConcreteCategory.hom g) ((CategoryTheory.ConcreteCategory.hom f) r)- Defined in
- Mathlib.Algebra.Category.Ring.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- RingHomstatement · cited by 10,189
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- CommRingCatstatement and proof · cited by 2,333
- CommRingCat.carrierstatement and proof · cited by 1,096
- CommRingCat.Hom.homproof · cited by 432
Cited by15
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.normalizationDesc_compproof · cited by 5
- AlgebraicGeometry.LocallyRingedSpace.evaluation_naturalityproof · cited by 4
- AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen'proof · cited by 2
- AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coordproof · cited by 1
- AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpenproof · cited by 1
- AlgebraicGeometry.sourceAffineLocally_isLocalproof · cited by 1
- AlgebraicGeometry.eq_zero_of_basicOpen_eq_botproof · cited by 1
- AlgebraicGeometry.isBasis_preimage_isAffineOpenproof · cited by 1
- AlgebraicGeometry.RingedSpace.basicOpen_res_eqproof · cited by 1
- AlgebraicGeometry.Scheme.basicOpen_appLEproof · cited by 0