Theorems · Definition · category theory

CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F G : CategoryTheory.Functor J C} →
          {s : CategoryTheory.Limits.Cone F} →
            {t : CategoryTheory.Limits.Cone G} →
              CategoryTheory.Limits.IsLimit s → CategoryTheory.Limits.IsLimit t → (F ≅ G) → (s.pt ≅ t.pt)

The cone points of two limit cones for naturally isomorphic functors are themselves isomorphic.

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

12 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category