Theorems · Theorem · commutative algebra

IsBaseChange.endHom_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] {P : Type u_5} [inst_5 : AddCommMonoid P] [inst_6 : Module R P]
  [inst_7 : Module S P] [inst_8 : IsScalarTower R S P] {α : M →ₗ[R] P} (j : IsBaseChange S α) (f : M →ₗ[R] M) (p : P),
  (j.endHom f) p = ((LinearMap.liftBaseChangeEquiv S) (α ∘ₗ f)) (j.equiv.symm p)

Defined in

Mathlib.RingTheory.TensorProduct.IsBaseChangeHom

Cited by

2 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTower