Theorems · Theorem · commutative algebra

IsBaseChange.linearMapLeftRight

∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_2} [inst_1 : CommSemiring S] [inst_2 : Algebra R S] {M : Type u_3}
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] {N : Type u_4} [inst_5 : AddCommMonoid N] [inst_6 : Module R N]
  {P : Type u_5} [inst_7 : AddCommMonoid P] [inst_8 : Module R P] {Q : Type u_6} [inst_9 : AddCommMonoid Q]
  [inst_10 : Module R Q] [inst_11 : Module S P] [inst_12 : IsScalarTower R S P] [inst_13 : Module S Q]
  [inst_14 : IsScalarTower R S Q] [Module.Free R M] [Module.Finite R M] {α : M →ₗ[R] P} (j : IsBaseChange S α)
  {β : N →ₗ[R] Q}, IsBaseChange S β → IsBaseChange S (j.linearMapLeftRightHom β)

Defined in

Mathlib.RingTheory.TensorProduct.IsBaseChangeHom

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTowerModuleIsScalarTowerModule.FreeModule.Finite