Theorems · Definition · category theory

CategoryTheory.Functor.effectiveEpiOver

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        (F : CategoryTheory.Functor C D) → [inst_2 : F.EffectivelyEnough] → (X : D) → F.effectiveEpiOverObj X ⟶ X

The epimorphism F.effectiveEpiOver : F.effectiveEpiOverObj X ⟶ X from the arbitrarily chosen object in the image of F over X.

Defined in

Mathlib.CategoryTheory.EffectiveEpi.Enough

Cited by

4 results in Mathlib

Foundations

Depth 5 from the axioms · uses Classical.choice

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.EffectivelyEnough