Theorems · Definition · category theory

CategoryTheory.Limits.IsLimit.homEquiv

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F : CategoryTheory.Functor J C} →
          {t : CategoryTheory.Limits.Cone F} →
            CategoryTheory.Limits.IsLimit t → {W : C} → (W ⟶ t.pt) ≃ ((CategoryTheory.Functor.const J).obj W ⟶ F)

The universal property of a limit cone: a map W ⟶ t.pt is the same as a cone on F with cone point W.

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

4 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category