Theorems · Definition · category theory

CategoryTheory.Limits.HasColimit.isoOfNatIso

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u} →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        {F G : CategoryTheory.Functor J C} →
          [inst_2 : CategoryTheory.Limits.HasColimit F] →
            [inst_3 : CategoryTheory.Limits.HasColimit G] →
              (F ≅ G) → (CategoryTheory.Limits.colimit F ≅ CategoryTheory.Limits.colimit G)

The colimits of F : J ⥤ C and G : J ⥤ C are isomorphic, if the functors are naturally isomorphic.

Defined in

Mathlib.CategoryTheory.Limits.HasLimits

Cited by

56 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitCategoryTheory.Limits.HasColimit