Theorems · Definition · nonassociative algebras

LieHom.prod

{R : Type u_1} →
  {L₁ : Type u_2} →
    {L₂ : Type u_3} →
      {L : Type u_4} →
        [inst : CommRing R] →
          [inst_1 : LieRing L₁] →
            [inst_2 : LieAlgebra R L₁] →
              [inst_3 : LieRing L₂] →
                [inst_4 : LieAlgebra R L₂] →
                  [inst_5 : LieRing L] → [inst_6 : LieAlgebra R L] → (L →ₗ⁅R⁆ L₁) → (L →ₗ⁅R⁆ L₂) → L →ₗ⁅R⁆ L₁ × L₂

The prod of two Lie algebra homomorphisms is a Lie algebra homomorphism.

Defined in

Mathlib.Algebra.Lie.Prod

Cited by

8 results in Mathlib

Foundations

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

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebraLieRingLieAlgebra