Theorems · Definition · category theory

CategoryTheory.Limits.colimit.isColimit

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u} →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        (F : CategoryTheory.Functor J C) →
          [inst_2 : CategoryTheory.Limits.HasColimit F] →
            CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.colimit.cocone F)

Evidence that the arbitrary choice of cocone is a colimit cocone.

Defined in

Mathlib.CategoryTheory.Limits.HasLimits

Cited by

193 results in Mathlib

Foundations

Depth 6 from the axioms, rests on 12 definitions · uses Classical.choice

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimit