Theorems · Definition · nonassociative algebras

LieSubmodule.inclusion

{R : Type u} →
  {L : Type v} →
    {M : Type w} →
      [inst : CommRing R] →
        [inst_1 : LieRing L] →
          [inst_2 : AddCommGroup M] →
            [inst_3 : Module R M] → [inst_4 : LieRingModule L M] → {N N' : LieSubmodule R L M} → N ≤ N' → ↥N →ₗ⁅R,L⁆ ↥N'

Given two nested Lie submodules N ⊆ N', the inclusion N ↪ N' is a morphism of Lie modules.

Defined in

Mathlib.Algebra.Lie.Submodule

Cited by

4 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModule