Theorems · Definition · nonassociative algebras

LieRinehartAlgebra.Hom.comp

{R : Type u_1} →
  {A₁ : Type u_2} →
    {L₁ : Type u_3} →
      {A₂ : Type u_4} →
        {L₂ : Type u_5} →
          {A₃ : Type u_6} →
            {L₃ : Type u_7} →
              [inst : CommRing R] →
                [inst_1 : CommRing A₁] →
                  [inst_2 : LieRing L₁] →
                    [inst_3 : Module A₁ L₁] →
                      [inst_4 : LieRingModule L₁ A₁] →
                        [inst_5 : CommRing A₂] →
                          [inst_6 : LieRing L₂] →
                            [inst_7 : Module A₂ L₂] →
                              [inst_8 : LieRingModule L₂ A₂] →
                                [inst_9 : CommRing A₃] →
                                  [inst_10 : LieRing L₃] →
                                    [inst_11 : Module A₃ L₃] →
                                      [inst_12 : LieRingModule L₃ A₃] →
                                        [inst_13 : Algebra R A₁] →
                                          [inst_14 : LieAlgebra R L₁] →
                                            [inst_15 : Algebra R A₂] →
                                              [inst_16 : LieAlgebra R L₂] →
                                                [inst_17 : Algebra R A₃] →
                                                  [inst_18 : LieAlgebra R L₃] →
                                                    {σ₁₂ : A₁ →ₐ[R] A₂} →
                                                      {σ₂₃ : A₂ →ₐ[R] A₃} →
                                                        LieRinehartAlgebra.Hom σ₁₂ L₁ L₂ →
                                                          LieRinehartAlgebra.Hom σ₂₃ L₂ L₃ →
                                                            LieRinehartAlgebra.Hom (σ₂₃.comp σ₁₂) L₁ L₃

The composition of Lie-Rinehart algebra morphisms is again a morphism.

Defined in

Mathlib.Algebra.LieRinehartAlgebra.Defs

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommRingCommRingLieRingModuleLieRingModuleCommRingLieRingModuleLieRingModuleCommRingLieRingModuleLieRingModuleAlgebraLieAlgebraAlgebraLieAlgebraAlgebraLieAlgebra