Theorems · Theorem · nonassociative algebras

LieSubmodule.map_comap_eq

∀ {R : Type u} {L : Type v} {M : Type w} {M₂ : 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 M₂]
  [inst_6 : Module R M₂] [inst_7 : LieRingModule L M₂] (N₂ : LieSubmodule R L M₂) (f : M →ₗ⁅R,L⁆ M₂),
  N₂ ≤ f.range → LieSubmodule.map f (LieSubmodule.comap f N₂) = N₂

Defined in

Mathlib.Algebra.Lie.IdealOperations

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingLieRingAddCommGroupModuleLieRingModuleAddCommGroupModuleLieRingModule