Theorems · Theorem · commutative algebra
Algebra.Etale.comp
∀ (R : Type u) (A : Type v) (B : Type u_1) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] [inst_3 : CommRing B] [inst_4 : Algebra R B] [inst_5 : Algebra A B] [IsScalarTower R A B] [Algebra.Etale R A] [Algebra.Etale A B], Algebra.Etale R B
Étale is stable under composition.
- Defined in
- Mathlib.RingTheory.Etale.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- IsScalarTowerstatement and proof · cited by 3,896
- Algebra.Etalestatement and proof · cited by 34
- Algebra.FinitePresentation.transproof · cited by 8
- Algebra.FormallyEtale.compproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.IsFiniteSplit.exists_tensorProduct_of_etaleproof · cited by 0