Theorems · Definition · nonassociative algebras

LieHom.prodMap

{R : Type u_1} →
  {L₁ : Type u_2} →
    {L₂ : Type u_3} →
      {L₃ : Type u_5} →
        {L₄ : Type u_6} →
          [inst : CommRing R] →
            [inst_1 : LieRing L₁] →
              [inst_2 : LieAlgebra R L₁] →
                [inst_3 : LieRing L₂] →
                  [inst_4 : LieAlgebra R L₂] →
                    [inst_5 : LieRing L₃] →
                      [inst_6 : LieAlgebra R L₃] →
                        [inst_7 : LieRing L₄] →
                          [inst_8 : LieAlgebra R L₄] → (L₁ →ₗ⁅R⁆ L₃) → (L₂ →ₗ⁅R⁆ L₄) → L₁ × L₂ →ₗ⁅R⁆ L₃ × L₄

Prod.map of two Lie algebra homomorphisms.

Defined in

Mathlib.Algebra.Lie.Prod

Cited by

6 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebraLieRingLieAlgebraLieRingLieAlgebra