Theorems · Definition · category theory

CategoryTheory.Limits.HasLimit.isoOfEquivalence

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {K : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} K] →
        {C : Type u} →
          [inst_2 : CategoryTheory.Category.{v, u} C] →
            {F : CategoryTheory.Functor J C} →
              [inst_3 : CategoryTheory.Limits.HasLimit F] →
                {G : CategoryTheory.Functor K C} →
                  [inst_4 : CategoryTheory.Limits.HasLimit G] →
                    (e : J ≌ K) →
                      (e.functor.comp G ≅ F) → (CategoryTheory.Limits.limit F ≅ CategoryTheory.Limits.limit G)

The limits of F : J ⥤ C and G : K ⥤ C are isomorphic, if there is an equivalence e : J ≌ K making the triangle commute up to natural isomorphism.

Defined in

Mathlib.CategoryTheory.Limits.HasLimits

Cited by

8 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitCategoryTheory.Limits.HasLimit