Theorems · Theorem · ring theory

Algebra.TensorProduct.map_comp_includeLeft

∀ {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.includeLeft = Algebra.TensorProduct.includeLeft.comp f

Defined in

Mathlib.RingTheory.TensorProduct.Maps

Cited by

7 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraSemiringAlgebraAlgebraIsScalarTowerSemiringAlgebraSemiringAlgebraAlgebraIsScalarTowerSemiringAlgebra