Theorems · Theorem · nonassociative algebras

LieModuleEquiv.right_inv

∀ {R : Type u} {L : Type v} {M : Type w} {N : Type w₁} [inst : CommRing R] [inst_1 : LieRing L]
  [inst_2 : AddCommGroup M] [inst_3 : AddCommGroup N] [inst_4 : Module R M] [inst_5 : Module R N]
  [inst_6 : LieRingModule L M] [inst_7 : LieRingModule L N] (self : M ≃ₗ⁅R,L⁆ N),
  Function.RightInverse self.invFun (↑self.toLieModuleHom).toFun

The inverse function of an equivalence of Lie modules is a right inverse of the underlying function.

Defined in

Mathlib.Algebra.Lie.Basic

Cited by

0 results in Mathlib

Foundations

Depth 14 from the axioms · uses no axioms

Assumes

CommRingLieRingAddCommGroupAddCommGroupModuleModuleLieRingModuleLieRingModule