Theorems · Theorem · commutative algebra

LinearMap.rTensor_comp_lTensor

∀ {R : Type u_1} [inst : CommSemiring R] (M : Type u_7) {N : Type u_8} {P : Type u_9} {Q : Type u_10}
  [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid N] [inst_3 : AddCommMonoid P] [inst_4 : AddCommMonoid Q]
  [inst_5 : Module R M] [inst_6 : Module R N] [inst_7 : Module R P] [inst_8 : Module R Q] (f : M →ₗ[R] P)
  (g : N →ₗ[R] Q), LinearMap.rTensor Q f ∘ₗ LinearMap.lTensor M g = TensorProduct.map f g

Defined in

Mathlib.LinearAlgebra.TensorProduct.Map

Cited by

13 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModule