Theorems · Theorem · linear algebra

TensorProduct.AlgebraTensorModule.congr_trans

∀ {R : Type uR} {A : Type uA} {M : Type uM} {N : Type uN} {P : Type uP} {Q : Type uQ} {P' : Type uP'} {Q' : Type uQ'}
  [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] [inst_3 : AddCommMonoid M] [inst_4 : Module R M]
  [inst_5 : Module A M] [inst_6 : IsScalarTower R A M] [inst_7 : AddCommMonoid N] [inst_8 : Module R N]
  [inst_9 : AddCommMonoid P] [inst_10 : Module R P] [inst_11 : Module A P] [inst_12 : IsScalarTower R A P]
  [inst_13 : AddCommMonoid Q] [inst_14 : Module R Q] [inst_15 : AddCommMonoid P'] [inst_16 : Module R P']
  [inst_17 : Module A P'] [inst_18 : IsScalarTower R A P'] [inst_19 : AddCommMonoid Q'] [inst_20 : Module R Q']
  (f₁ : M ≃ₗ[A] P) (f₂ : P ≃ₗ[A] P') (g₁ : N ≃ₗ[R] Q) (g₂ : Q ≃ₗ[R] Q'),
  TensorProduct.AlgebraTensorModule.congr (f₁ ≪≫ₗ f₂) (g₁ ≪≫ₗ g₂) =
    TensorProduct.AlgebraTensorModule.congr f₁ g₁ ≪≫ₗ TensorProduct.AlgebraTensorModule.congr f₂ g₂

Defined in

Mathlib.LinearAlgebra.TensorProduct.Tower

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModule