Theorems · Definition · category theory

CategoryTheory.Limits.IsColimit.ofCoconeEquiv

{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] →
            {F : CategoryTheory.Functor J C} →
              {D : Type u₄} →
                [inst_3 : CategoryTheory.Category.{v₄, u₄} D] →
                  {G : CategoryTheory.Functor K D} →
                    (h : CategoryTheory.Limits.Cocone G ≌ CategoryTheory.Limits.Cocone F) →
                      {c : CategoryTheory.Limits.Cocone G} →
                        CategoryTheory.Limits.IsColimit (h.functor.obj c) ≃ CategoryTheory.Limits.IsColimit c

Given two functors which have equivalent categories of cocones, we can transport a colimiting cocone across the equivalence.

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

3 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category