Theorems · Definition · category theory

CategoryTheory.Limits.IsLimit.ofPointIso

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F : CategoryTheory.Functor J C} →
          {r t : CategoryTheory.Limits.Cone F} →
            (P : CategoryTheory.Limits.IsLimit r) →
              [i : CategoryTheory.IsIso (P.lift t)] → CategoryTheory.Limits.IsLimit t

If the canonical morphism from a cone point to a limiting cone point is an iso, then the first cone was limiting also.

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

9 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.IsIso