Theorems · Definition · commutative algebra
Algebra.tensorH1CotangentOfFlat
(R : Type u_1) →
(S : Type u_2) →
[inst : CommRing R] →
[inst_1 : CommRing S] →
[inst_2 : Algebra R S] →
(T : Type u_3) →
[inst_3 : CommRing T] →
[inst_4 : Algebra R T] →
[Module.Flat R T] →
TensorProduct R T (Algebra.H1Cotangent R S) ≃ₗ[T] Algebra.H1Cotangent T (TensorProduct R T S)Flat base change commutes with H1Cotangent.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearEquivstatement · cited by 3,317
- TensorProductstatement · cited by 2,545
- LinearEquiv.transproof · cited by 298
- Module.Flatstatement and proof · cited by 279
- Algebra.Generators.toExtensionstatement and proof · cited by 103
- LinearEquiv.restrictScalarsproof · cited by 46
- Algebra.H1Cotangentstatement · cited by 27
- Algebra.Generators.selfstatement and proof · cited by 22
- Algebra.Generators.baseChangeproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.Smooth.of_smooth_tensorProduct_of_faithfullyFlatproof · cited by 2
- Algebra.tensorH1CotangentOfFlat_tmulstatement · cited by 0