Theorems · Theorem · category theory

CategoryTheory.Functor.PreservesEpimorphisms.preserves

∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {D : Type u₂} {inst_1 : CategoryTheory.Category.{v₂, u₂} D}
  {F : CategoryTheory.Functor C D} [self : F.PreservesEpimorphisms] {X Y : C} (f : X ⟶ Y) [CategoryTheory.Epi f],
  CategoryTheory.Epi (F.map f)

A functor preserves epimorphisms if it maps epimorphisms to epimorphisms.

Defined in

Mathlib.CategoryTheory.Functor.EpiMono

Cited by

2 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

CategoryTheory.Functor.PreservesEpimorphismsCategoryTheory.Epi