Theorems · Definition · algebraic geometry
CommAlgCat.FiniteEtale.equivOfIsSepClosed
(Ω : Type u) → [inst : Field Ω] → [IsSepClosed Ω] → (CommAlgCat.FiniteEtale Ω)ᵒᵖ ≌ FintypeCat
If Ω is a separably closed field, the category of finite étale Ω-algebras is
anti-equivalent to FintypeCat.
- Defined in
- Mathlib.RingTheory.Etale.Finite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsSepClosed
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- Oppositestatement and proof · cited by 8,081
- Fieldstatement and proof · cited by 7,404
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- Equiv.symmproof · cited by 3,681
- CategoryTheory.Functor.idproof · cited by 3,333
- Finitestatement · cited by 3,029
- Opposite.unopproof · cited by 2,231
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
Cited by3
Results whose statement or proof uses this declaration.
- CommAlgCat.FiniteEtale.equivOfIsSepClosed_functorstatement and proof · cited by 0
- CommAlgCat.FiniteEtale.equivOfIsSepClosed_inverse_mapstatement and proof · cited by 0
- CommAlgCat.FiniteEtale.equivOfIsSepClosed_inverse_objstatement and proof · cited by 0