Theorems · Theorem · group theory

Representation.smul_ofModule_asModule

∀ {k : Type u_1} {G : Type u_2} [inst : CommSemiring k] [inst_1 : Monoid G] (M : Type u_4) [inst_2 : AddCommMonoid M]
  [inst_3 : Module (MonoidAlgebra k G) M] (r : MonoidAlgebra k G) (m : (Representation.ofModule M).asModule),
  (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) ((Representation.ofModule M).asModuleEquiv (r • m)) =
    r • (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) ((Representation.ofModule M).asModuleEquiv m)

Defined in

Mathlib.RepresentationTheory.Basic

Cited by

0 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidModule