Theorems · Theorem · nonassociative algebras

LieSubmodule.Quotient.lieModuleHom_ext

∀ {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 : LieSubmodule R L M) [inst_5 : LieAlgebra R L]
  [inst_6 : LieModule R L M] ⦃f g : M ⧸ N →ₗ⁅R,L⁆ M⦄,
  f.comp (LieSubmodule.Quotient.mk' N) = g.comp (LieSubmodule.Quotient.mk' N) → f = g

Two LieModuleHoms from a quotient lie module are equal if their compositions with LieSubmodule.Quotient.mk' are equal. See note [partially-applied ext lemmas].

Defined in

Mathlib.Algebra.Lie.Quotient

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModuleLieAlgebraLieModule