Theorems · Definition · category theory

CategoryTheory.Limits.isColimitOfIsColimitCoforkMap

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (G : CategoryTheory.Functor C D) →
          {X Y Z : C} →
            {f g : X ⟶ Y} →
              {h : Y ⟶ Z} →
                (w : CategoryTheory.CategoryStruct.comp f h = CategoryTheory.CategoryStruct.comp g h) →
                  [CategoryTheory.Limits.ReflectsColimit (CategoryTheory.Limits.parallelPair f g) G] →
                    CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.Cofork.ofπ (G.map h) ⋯) →
                      CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.Cofork.ofπ h w)

The property of reflecting coequalizers expressed in terms of coforks.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.ReflectsColimit