Theorems · Theorem · ring theory

SemilinearMapClass.map_smul_inv

∀ {R : Type u_1} {S : Type u_5} {M : Type u_8} {M₃ : Type u_11} {F : Type u_14} [inst : Semiring R]
  [inst_1 : Semiring S] [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₃] [inst_4 : Module R M]
  [inst_5 : Module S M₃] {σ : R →+* S} (f : F) [inst_6 : FunLike F M M₃] [SemilinearMapClass F σ M M₃] {σ' : S →+* R}
  [RingHomInvPair σ σ'] (c : S) (x : M), c • f x = f (σ' c • x)

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

0 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleFunLikeSemilinearMapClassRingHomInvPair