Theorems · Definition · nonassociative algebras

LieHom.rangeRestrict

{R : Type u} →
  {L : Type v} →
    [inst : CommRing R] →
      [inst_1 : LieRing L] →
        [inst_2 : LieAlgebra R L] →
          {L₂ : Type w} → [inst_3 : LieRing L₂] → [inst_4 : LieAlgebra R L₂] → (f : L →ₗ⁅R⁆ L₂) → L →ₗ⁅R⁆ ↥f.range

We can restrict a morphism to a (surjective) map to its range.

Defined in

Mathlib.Algebra.Lie.Subalgebra

Cited by

3 results in Mathlib

Foundations

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

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra