Theorems · Theorem · nonassociative algebras

RootPairing.Hom.comp_coweightMap_apply

∀ {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] {ι₁ : Type u_5} {M₁ : Type u_6} {N₁ : Type u_7}
  {ι₂ : Type u_8} {M₂ : Type u_9} {N₂ : Type u_10} [inst_5 : AddCommGroup M₁] [inst_6 : Module R M₁]
  [inst_7 : AddCommGroup N₁] [inst_8 : Module R N₁] [inst_9 : AddCommGroup M₂] [inst_10 : Module R M₂]
  [inst_11 : AddCommGroup N₂] [inst_12 : Module R N₂] {P : RootPairing ι R M N} {P₁ : RootPairing ι₁ R M₁ N₁}
  {P₂ : RootPairing ι₂ R M₂ N₂} (g : P₁.Hom P₂) (f : P.Hom P₁) (x : N₂),
  (g.comp f).coweightMap x = f.coweightMap (g.coweightMap x)

Defined in

Mathlib.LinearAlgebra.RootSystem.Hom

Cited by

7 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleAddCommGroupModuleAddCommGroupModuleAddCommGroupModuleAddCommGroupModule