Theorems · Theorem · commutative algebra

LinearMap.rTensor_comp_apply

∀ {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] (g : P →ₗ[R] Q)
  (f : N →ₗ[R] P) (x : TensorProduct R N M),
  (LinearMap.rTensor M (g ∘ₗ f)) x = (LinearMap.rTensor M g) ((LinearMap.rTensor M f) x)

Defined in

Mathlib.LinearAlgebra.TensorProduct.Map

Cited by

7 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModule