English
There is a morphism associated to multiplication on the right in G, giving a map from the tensor product of rightFDRep to rightFDRep, compatible with the monoidal structure.
Русский
Существует гомоморф, связанный с правым умножением в G, который задает отображение между тензорным произведением и правым FDRep.
LaTeX
$$harom: rightFDRep ⊗ rightFDRep ⟶ rightFDRep with hom := ofHom (LinearMap.mul' k (G → k)) and commutativity condition.$$
Lean4
/-- The group homomorphism `G →* Aut (forget k G)` shown to be an isomorphism. -/
@[simps]
def equivHom : G →* Aut (forget k G)
where
toFun g := LaxMonoidalFunctor.isoOfComponents (equivApp g) (fun f ↦ (f.comm g).symm) rfl (by intros; rfl)
map_one' := by ext; simp; rfl
map_mul' _ _ := by ext; simp; rfl
