Theorems · Definition · category theory

CategoryTheory.Limits.IsColimit.ofReflectsCoconeInitial

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {K : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} K] →
        {C : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
            {D : Type u₄} →
              [inst_3 : CategoryTheory.Category.{v₄, u₄} D] →
                {F : CategoryTheory.Functor J C} →
                  {F' : CategoryTheory.Functor K D} →
                    (G : CategoryTheory.Functor (CategoryTheory.Limits.Cocone F) (CategoryTheory.Limits.Cocone F')) →
                      [CategoryTheory.Limits.ReflectsColimit
                            (CategoryTheory.Functor.empty (CategoryTheory.Limits.Cocone F)) G] →
                        {c : CategoryTheory.Limits.Cocone F} →
                          CategoryTheory.Limits.IsColimit (G.obj c) → CategoryTheory.Limits.IsColimit c

If G : Cocone F ⥤ Cocone F' reflects initial objects, it reflects colimit cocones.

Defined in

Mathlib.CategoryTheory.Limits.ConeCategory

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.ReflectsColimit