Theorems · Theorem · ring theory
Algebra.TensorProduct.map_comp_includeLeftRingHom
∀ {R : Type uR} {S : Type uS} {A : Type uA} {B : Type uB} {C : Type uC} {D : Type uD} [inst : CommSemiring R]
[inst_1 : CommSemiring S] [inst_2 : Algebra R S] [inst_3 : Semiring A] [inst_4 : Algebra R A] [inst_5 : Algebra S A]
[inst_6 : IsScalarTower R S A] [inst_7 : Semiring B] [inst_8 : Algebra R B] [inst_9 : Semiring C]
[inst_10 : Algebra R C] [inst_11 : Algebra S C] [inst_12 : IsScalarTower R S C] [inst_13 : Semiring D]
[inst_14 : Algebra R D] (f : A →ₐ[S] C) (g : B →ₐ[R] D),
(↑(Algebra.TensorProduct.map f g)).comp Algebra.TensorProduct.includeLeftRingHom =
Algebra.TensorProduct.includeLeftRingHom.comp ↑f- Defined in
- Mathlib.RingTheory.TensorProduct.Maps
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Quot.sound
Around this declaration
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.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomstatement and proof · cited by 3,236
- TensorProductstatement · cited by 2,545
- TensorProduct.tmulproof · cited by 1,182
- RingHom.compstatement · cited by 899
- map_oneproof · cited by 861
- RingHomClass.toRingHomstatement · cited by 746
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.mono_pushoutSection_of_iSup_eqproof · cited by 2
- RingHom.Flat.mapOfCompatibleSMulproof · cited by 1