English
Equality of two liftNCAlgHom constructed from data f,g,h_comm reduces to equality of their underlying actions on basis elements.
Русский
Сходство двух liftNCAlgHom, построенных из f,g,h_comm, сводится к равенству их действий на базисных элементах.
LaTeX
$$liftNCAlgHom f g h_comm = liftNCAlgHom f' g' h_comm' iff соответствующие действия совпадают$$
Lean4
/-- Any monoid homomorphism `G →* A` can be lifted to an algebra homomorphism
`MonoidAlgebra k G →ₐ[k] A`. -/
def lift : (G →* A) ≃ (MonoidAlgebra k G →ₐ[k] A)
where
invFun f := (f : MonoidAlgebra k G →* A).comp (of k G)
toFun F := liftNCAlgHom (Algebra.ofId k A) F fun _ _ => Algebra.commutes _ _
left_inv
f := by
ext
simp [liftNCAlgHom, liftNCRingHom]
right_inv
F := by
ext
simp [liftNCAlgHom, liftNCRingHom]
