Theorems · Definition · nonassociative algebras

LieEquiv.ofBijective

{R : Type u} →
  {L₁ : Type v} →
    {L₂ : Type w} →
      [inst : CommRing R] →
        [inst_1 : LieRing L₁] →
          [inst_2 : LieRing L₂] →
            [inst_3 : LieAlgebra R L₁] →
              [inst_4 : LieAlgebra R L₂] → (f : L₁ →ₗ⁅R⁆ L₂) → Function.Bijective ⇑f → L₁ ≃ₗ⁅R⁆ L₂

A bijective morphism of Lie algebras yields an equivalence of Lie algebras.

Defined in

Mathlib.Algebra.Lie.Basic

Cited by

2 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieRingLieAlgebraLieAlgebra