Theorems · Theorem · commutative algebra
KaehlerDifferential.DLinearMap_apply
∀ (R : Type u) (S : Type v) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (s : S), (KaehlerDifferential.DLinearMap R S) s = (KaehlerDifferential.ideal R S).toCotangent ⟨1 ⊗ₜ[R] s - s ⊗ₜ[R] 1, ⋯⟩
- Defined in
- Mathlib.RingTheory.Kaehler.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Idealstatement · cited by 4,748
- TensorProductstatement · cited by 2,545
- TensorProduct.tmulstatement · cited by 1,182
- KaehlerDifferentialstatement · cited by 204
- Ideal.Cotangentstatement · cited by 68
- Ideal.toCotangentstatement · cited by 45
- KaehlerDifferential.idealstatement · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- KaehlerDifferential.span_range_derivationproof · cited by 7