Theorems · Definition · category theory

CategoryTheory.Limits.coconeOfIsSplitEpi

{C : Type u} →
  {X Y : C} →
    [inst : CategoryTheory.Category.{v, u} C] →
      (f : X ⟶ Y) →
        [inst_1 : CategoryTheory.IsSplitEpi f] →
          CategoryTheory.Limits.Cofork (CategoryTheory.CategoryStruct.id X)
            (CategoryTheory.CategoryStruct.comp f (CategoryTheory.section_ f))

A split epi f coequalizes (f ≫ section_ f) and (𝟙 X). Here we build the cocone, and show in isSplitEpiCoequalizes that it is a colimit cocone.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Equalizers

Cited by

3 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsSplitEpi