Theorems · Theorem · nonassociative algebras

RootPairing.Hom.root_weightMap

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] {ι₂ : Type u_5} {M₂ : Type u_6} {N₂ : Type u_7}
  [inst_5 : AddCommGroup M₂] [inst_6 : Module R M₂] [inst_7 : AddCommGroup N₂] [inst_8 : Module R N₂]
  {P : RootPairing ι R M N} {Q : RootPairing ι₂ R M₂ N₂} (self : P.Hom Q),
  ⇑self.weightMap ∘ ⇑P.root = ⇑Q.root ∘ ⇑self.indexEquiv

Defined in

Mathlib.LinearAlgebra.RootSystem.Hom

Cited by

2 results in Mathlib

Foundations

Depth 21 from the axioms · uses Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleAddCommGroupModuleAddCommGroupModule