Theorems · Theorem · linear algebra

LinearMap.rTensor_exact_iff_lTensor_exact

∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_2} {N : Type u_3} {P : Type u_4} (Q : Type u_5)
  [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] N}
  {g : N →ₗ[R] P},
  Function.Exact ⇑(LinearMap.rTensor Q f) ⇑(LinearMap.rTensor Q g) ↔
    Function.Exact ⇑(LinearMap.lTensor Q f) ⇑(LinearMap.lTensor Q g)

Defined in

Mathlib.LinearAlgebra.TensorProduct.RightExactness

Cited by

1 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModule