Theorems · Definition · nonassociative algebras

LieSubmodule.mapOrderEmbedding

{R : Type u} →
  {L : Type v} →
    {M : Type w} →
      {M' : Type w₁} →
        [inst : CommRing R] →
          [inst_1 : LieRing L] →
            [inst_2 : AddCommGroup M] →
              [inst_3 : Module R M] →
                [inst_4 : LieRingModule L M] →
                  [inst_5 : AddCommGroup M'] →
                    [inst_6 : Module R M'] →
                      [inst_7 : LieRingModule L M'] →
                        {f : M →ₗ⁅R,L⁆ M'} → Function.Injective ⇑f → LieSubmodule R L M ↪o LieSubmodule R L M'

An injective morphism of Lie modules embeds the lattice of submodules of the domain into that of the target.

Defined in

Mathlib.Algebra.Lie.Submodule

Cited by

3 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModuleAddCommGroupModuleLieRingModule