Theorems · Definition · category theory

CategoryTheory.Functor.IsEventuallyConstantTo.isLimitCone

{J : Type u_1} →
  {C : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} J] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} C] →
        {F : CategoryTheory.Functor J C} →
          {i₀ : J} →
            (h : F.IsEventuallyConstantTo i₀) →
              [inst_2 : CategoryTheory.IsCofiltered J] → CategoryTheory.Limits.IsLimit h.cone

When h : F.IsEventuallyConstantTo i₀, the limit of F exists and is F.obj i₀.

Defined in

Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant

Cited by

2 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.IsCofiltered