Theorems · Theorem · commutative algebra
CommRingCat.hom_comp
∀ {R S T : CommRingCat} (f : R ⟶ S) (g : S ⟶ T),
CommRingCat.Hom.hom (CategoryTheory.CategoryStruct.comp f g) = (CommRingCat.Hom.hom g).comp (CommRingCat.Hom.hom f)- Defined in
- Mathlib.Algebra.Category.Ring.Basic
- Cited by
- 27 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.
Cites7
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.CategoryStruct.compstatement · cited by 17,999
- RingHomstatement · cited by 10,189
- CommRingCatstatement and proof · cited by 2,333
- CommRingCat.carrierstatement · cited by 1,096
- RingHom.compstatement · cited by 899
- CommRingCat.Hom.homstatement · cited by 432
Cited by27
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.HasRingHomProperty.Spec_iffproof · cited by 19
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- AlgebraicGeometry.Scheme.Hom.le_ker_compproof · cited by 5
- AlgebraicGeometry.HasRingHomProperty.comp_of_isOpenImmersionproof · cited by 4
- AlgebraicGeometry.HasRingHomProperty.of_source_openCoverproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIsoproof · cited by 2
- RingHom.IsStableUnderBaseChange.pullback_fst_appTopproof · cited by 2
- AlgebraicGeometry.affineAnd_isLocalproof · cited by 2
- AlgebraicGeometry.IsAffineOpen.appLE_eq_away_mapproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.quasiFiniteAtproof · cited by 1
- CommRingCat.closure_range_union_range_eq_top_of_isPushoutproof · cited by 1
- AlgebraicGeometry.HasRingHomProperty.of_stalkMapproof · cited by 1