Theorems · Theorem · category theory

CategoryTheory.Functor.PreservesEffectiveEpis.preserves

∀ {C : Type u_1} {inst : CategoryTheory.Category.{v_1, u_1} C} {D : Type u_2}
  {inst_1 : CategoryTheory.Category.{v_2, u_2} D} {F : CategoryTheory.Functor C D} [self : F.PreservesEffectiveEpis]
  {X Y : C} (f : X ⟶ Y) [CategoryTheory.EffectiveEpi f], CategoryTheory.EffectiveEpi (F.map f)

A functor preserves effective epimorphisms if it maps effective epimorphisms to effective epimorphisms.

Defined in

Mathlib.CategoryTheory.EffectiveEpi.Preserves

Cited by

0 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

CategoryTheory.Functor.PreservesEffectiveEpisCategoryTheory.EffectiveEpi