Theorems · Theorem · linear algebra

lTensor_exact

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} {P : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : AddCommGroup N] [inst_3 : AddCommGroup P] [inst_4 : Module R M] [inst_5 : Module R N] [inst_6 : Module R P]
  {f : M →ₗ[R] N} {g : N →ₗ[R] P} (Q : Type u_5) [inst_7 : AddCommGroup Q] [inst_8 : Module R Q],
  Function.Exact ⇑f ⇑g → Function.Surjective ⇑g → Function.Exact ⇑(LinearMap.lTensor Q f) ⇑(LinearMap.lTensor Q g)

Tensoring an exact pair on the left gives an exact pair

Defined in

Mathlib.LinearAlgebra.TensorProduct.RightExactness

Cited by

11 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupAddCommGroupModuleModuleModuleAddCommGroupModule