Theorems · Theorem · algebraic geometry
CommAlgCat.FiniteEtale.finiteSpec_map
∀ (k : Type u) [inst : Field k] {X Y : (CommAlgCat.FiniteEtale k)ᵒᵖ} (f : X ⟶ Y),
(CommAlgCat.FiniteEtale.finiteSpec k).map f = FintypeCat.homMk (PrimeSpectrum.comap ↑(CommAlgCat.Hom.hom f.unop.hom))- Defined in
- Mathlib.RingTheory.Etale.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement and proof · cited by 8,081
- Fieldstatement and proof · cited by 7,404
- AlgHomstatement · cited by 3,236
- Finitestatement · cited by 3,029
- Opposite.unopstatement · cited by 2,231
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement · cited by 1,316
- Quiver.Hom.unopstatement · cited by 903
- CategoryTheory.InducedCategory.Hom.homstatement · cited by 850
- RingHomClass.toRingHomstatement · cited by 746
- CategoryTheory.ObjectProperty.FullSubcategorystatement · cited by 726
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