English
If S is the localization of R at r, there is a canonical submersive presentation of S as an R-algebra along with the unit object.
Русский
Если S — локализация R в элементе r, существует каноническое субмассовое представление S как R-алгебра с единичным объектом.
LaTeX
$$$\\text{localizationAway}(S,r) : \\text{SubmersivePresentation } R S\\;\\text{Unit} \\;\\text{Unit}$$$
Lean4
/-- Given an `R`-algebra `S` and an `S`-algebra `T` with submersive presentations,
this is the canonical submersive presentation of `T` as an `R`-algebra. -/
noncomputable def comp : SubmersivePresentation R T (ι' ⊕ ι) (σ' ⊕ σ)
where
__ := Q.toPreSubmersivePresentation.comp P.toPreSubmersivePresentation
jacobian_isUnit := by
rw [comp_jacobian_eq_jacobian_smul_jacobian, Algebra.smul_def, IsUnit.mul_iff]
exact ⟨RingHom.isUnit_map _ <| P.jacobian_isUnit, Q.jacobian_isUnit⟩
