Theorems · Theorem · commutative algebra
Algebra.SubmersivePresentation.cotangentEquiv_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) (x : P.toExtension.Cotangent)
(a : σ), P.cotangentEquiv x a = P.cotangentComplexAux x a- Cited by
- 1 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
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- Finitestatement and proof · cited by 3,029
- Algebra.Extension.Cotangentstatement and proof · cited by 121
- Algebra.Presentation.toGeneratorsstatement and proof · cited by 104
- Algebra.Generators.toExtensionstatement and proof · cited by 103
- Algebra.PreSubmersivePresentation.toPresentationstatement and proof · cited by 84
- Algebra.SubmersivePresentationstatement and proof · cited by 52
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.SubmersivePresentation.sectionCotangent_eq_iffproof · cited by 2