Theorems · Theorem · commutative algebra
Algebra.SubmersivePresentation.basisCotangent_apply
∀ {R : Type u_1} {S : Type u_2} {ι : Type u_3} {σ : Type u_4} [inst : CommRing R] [inst_1 : CommRing S]
[inst_2 : Algebra R S] [inst_3 : Finite σ] (P : Algebra.SubmersivePresentation R S ι σ) (r : σ),
P.basisCotangent r = Algebra.Extension.Cotangent.mk ⟨P.relation r, ⋯⟩- Cited by
- 2 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- Finitestatement and proof · cited by 3,029
- Module.Basisstatement · cited by 1,477
- Algebra.Extension.Ringstatement · cited by 179
- LinearEquiv.injectiveproof · cited by 162
- Algebra.Extension.Cotangentstatement · cited by 121
- LinearEquiv.apply_symm_applyproof · cited by 108
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.Generators.basisCotangentAway_applyproof · cited by 2
- Algebra.SubmersivePresentation.basisCotangent_localizationAway_applyproof · cited by 0