Theorems · Theorem · nonassociative algebras

LieSubalgebra.map_le_iff_le_comap

∀ {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} {K : LieSubalgebra R L} {K' : LieSubalgebra R L₂},
  LieSubalgebra.map f K ≤ K' ↔ K ≤ LieSubalgebra.comap f K'

Defined in

Mathlib.Algebra.Lie.Subalgebra

Cited by

2 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra