Theorems · Definition · nonassociative algebras

LieModuleEquiv.refl

{R : Type u} →
  {L : Type v} →
    {M : Type w} →
      [inst : CommRing R] →
        [inst_1 : LieRing L] →
          [inst_2 : AddCommGroup M] → [inst_3 : Module R M] → [inst_4 : LieRingModule L M] → M ≃ₗ⁅R,L⁆ M

Lie module equivalences are reflexive.

Defined in: Mathlib.Algebra.Lie.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Quot.sound
Assumes: CommRing LieRing AddCommGroup Module LieRingModule

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LieRingstatement and proof · cited by 1,548
LieRingModulestatement and proof · cited by 727
LieModuleEquivstatement · cited by 40

Cited by4

Results whose statement or proof uses this declaration.

LieModule.maxTrivEquiv_of_refl_eq_reflstatement and proof · cited by 0
LieModuleEquiv.symm_trans_selfstatement and proof · cited by 0
LieModuleEquiv.refl_applystatement · cited by 0
LieModuleEquiv.self_trans_symmstatement and proof · cited by 0