Theorems · Definition · nonassociative algebras

LieModuleHom.comp

{R : Type u} →
  {L : Type v} →
    {M : Type w} →
      {N : Type w₁} →
        {P : Type w₂} →
          [inst : CommRing R] →
            [inst_1 : LieRing L] →
              [inst_2 : AddCommGroup M] →
                [inst_3 : AddCommGroup N] →
                  [inst_4 : AddCommGroup P] →
                    [inst_5 : Module R M] →
                      [inst_6 : Module R N] →
                        [inst_7 : Module R P] →
                          [inst_8 : LieRingModule L M] →
                            [inst_9 : LieRingModule L N] →
                              [inst_10 : LieRingModule L P] → (N →ₗ⁅R,L⁆ P) → (M →ₗ⁅R,L⁆ N) → M →ₗ⁅R,L⁆ P

The composition of Lie module morphisms is a morphism.

Defined in

Mathlib.Algebra.Lie.Basic

Cited by

10 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingAddCommGroupAddCommGroupAddCommGroupModuleModuleModuleLieRingModuleLieRingModuleLieRingModule