Theorems · Theorem · category theory
CategoryTheory.PreGaloisCategory.surjective_on_fiber_of_epi
∀ {C : Type u₁} [inst : CategoryTheory.Category.{u₂, u₁} C] (F : CategoryTheory.Functor C FintypeCat)
[inst_1 : CategoryTheory.PreGaloisCategory C] [CategoryTheory.PreGaloisCategory.FiberFunctor F] {X Y : C} (f : X ⟶ Y)
[CategoryTheory.Epi f], Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom (F.map f))An epimorphism induces a surjective map on fibers.
- Defined in
- Mathlib.CategoryTheory.Galois.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- Finitestatement · cited by 3,029
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement · cited by 1,316
- TypeCat.Funstatement · cited by 1,307
- CategoryTheory.ObjectProperty.FullSubcategorystatement · cited by 726
- CategoryTheory.Epistatement and proof · cited by 688
Cited by1
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