Theorems · Definition · nonassociative algebras

LieHom.inverse

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

The inverse of a bijective morphism is a morphism.

Defined in

Mathlib.Algebra.Lie.Basic

Cited by

0 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra