Theorems · Definition · category theory

CategoryTheory.Limits.Cone.equivalenceOfReindexing

{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} →
              {G : CategoryTheory.Functor K C} →
                (e : K ≌ J) → (e.functor.comp F ≅ G) → (CategoryTheory.Limits.Cone F ≌ CategoryTheory.Limits.Cone G)

The categories of cones over F and G are equivalent if F and G are naturally isomorphic (possibly after changing the indexing category by an equivalence).

Defined in

Mathlib.CategoryTheory.Limits.Cones

Cited by

6 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category