Theorems · Theorem · commutative algebra
KaehlerDifferential.End_equiv_aux
∀ (R : Type u) (S : Type v) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
(f : S →ₐ[R] TensorProduct R S S ⧸ KaehlerDifferential.ideal R S ^ 2),
(Ideal.Quotient.mkₐ R (KaehlerDifferential.ideal R S).cotangentIdeal).comp f =
IsScalarTower.toAlgHom R S
((TensorProduct R S S ⧸ KaehlerDifferential.ideal R S ^ 2) ⧸ (KaehlerDifferential.ideal R S).cotangentIdeal) ↔
(Algebra.TensorProduct.lmul' R).kerSquareLift.comp f = AlgHom.id R S- Defined in
- Mathlib.RingTheory.Kaehler.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealstatement · cited by 4,748
- mul_oneproof · cited by 3,885
- AlgHomstatement and proof · cited by 3,236
- TensorProductstatement and proof · cited by 2,545
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.Quotient.mkproof · cited by 610
- AlgHom.compstatement and proof · cited by 501
- AlgHom.toRingHomstatement · cited by 490
Cited by1
Results whose statement or proof uses this declaration.
- KaehlerDifferential.endEquivAuxEquivproof · cited by 0