Theorems · Definition · nonassociative algebras

TensorProduct.LieModule.mapIncl

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

Given Lie submodules M' ⊆ M and N' ⊆ N, this is the natural map: M' ⊗ N' → M ⊗ N.

Defined in

Mathlib.Algebra.Lie.TensorProduct

Cited by

2 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleAddCommGroupModuleLieRingModuleLieModule