def Definition35_KahlerDifferentials (B : Type u_1) (A : Type u_2) [CommRing B] [CommRing A] [Algebra B A] : Type u_2

Definition 35 (Lecture 18). The module of Kähler differentials Ω[A⁄B] of a B-algebra A, providing the algebraic analogue of the cotangent bundle.

noncomputable def Definition35_universalDerivation (B : Type u_1) (A : Type u_2) [CommRing B] [CommRing A] [Algebra B A] : Derivation B A Ω[A⁄B]

The canonical universal B-linear derivation d : A → Ω[A⁄B] from Definition 35.

noncomputable def Definition35_universalProperty (B : Type u_1) (A : Type u_2) [CommRing B] [CommRing A] [Algebra B A] (M : Type u_3) [AddCommGroup M] [Module A M] [Module B M] [IsScalarTower B A M] : (Ω[A⁄B] →ₗ[A] M) ≃ₗ[A] Derivation B A M

Universal property of Kähler differentials (Definition 35): A-linear maps Ω[A⁄B] → M are in natural bijection with B-derivations A → M.