Theorems · Theorem · commutative algebra

IsBaseChange.linearMapLeftRightHom_comp_apply

∀ {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] {α : M →ₗ[R] P} (j : IsBaseChange S α) (β : N →ₗ[R] Q) (f : M →ₗ[R] N) (m : M),
  ((j.linearMapLeftRightHom β) f) (α m) = β (f m)

Defined in

Mathlib.RingTheory.TensorProduct.IsBaseChangeHom

Cited by

3 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTowerModuleIsScalarTower