Theorems · Definition · nonassociative algebras

RootPairing.Equiv.coweightEquiv

{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) → P.Equiv Q → N₂ ≃ₗ[R] N

The contravariant equivalence of coweight spaces given by an equivalence of root pairings.

Defined in

Mathlib.LinearAlgebra.RootSystem.Hom

Cited by

12 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleAddCommGroupModuleAddCommGroupModule