Theorems · Theorem · algebraic geometry
CommAlgCat.FiniteEtale.equivOfIsSepClosed_inverse_map
∀ (Ω : Type u) [inst : Field Ω] [inst_1 : IsSepClosed Ω] {X Y : FintypeCat} (f : X ⟶ Y),
(CommAlgCat.FiniteEtale.equivOfIsSepClosed Ω).inverse.map f =
(CommAlgCat.FiniteEtale.ofHom
(AlgHom.pi fun i => Pi.evalAlgHom Ω (fun a => Ω) ((CategoryTheory.ConcreteCategory.hom f) i))).op- Defined in
- Mathlib.RingTheory.Etale.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsSepClosed
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Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement · cited by 8,081
- Fieldstatement and proof · cited by 7,404
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- Finitestatement · cited by 3,029
- Quiver.Hom.opstatement · cited by 1,948
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement · cited by 1,316
- TypeCat.Funstatement · cited by 1,307
- CategoryTheory.Equivalence.inversestatement and proof · cited by 1,130
- CategoryTheory.ObjectProperty.FullSubcategorystatement · cited by 726
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