Theorems · Theorem · category theory

CategoryTheory.PreGaloisCategory.epi_of_nonempty_of_isConnected

∀ {C : Type u₁} [inst : CategoryTheory.Category.{u₂, u₁} C] (F : CategoryTheory.Functor C FintypeCat)
  [inst_1 : CategoryTheory.PreGaloisCategory C] [CategoryTheory.PreGaloisCategory.FiberFunctor F] {X A : C}
  [CategoryTheory.PreGaloisCategory.IsConnected A] [h : Nonempty (F.obj X).obj] (f : X ⟶ A), CategoryTheory.Epi f

A morphism from an object X with non-empty fiber to a connected object A is an epimorphism.

Defined in

Mathlib.CategoryTheory.Galois.Basic

Cited by

1 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreGaloisCategoryCategoryTheory.PreGaloisCategory.FiberFunctorCategoryTheory.PreGaloisCategory.IsConnectedNonempty