Theorems · Definition · category theory

CategoryTheory.Limits.colimit.isColimitToOver

{J : Type w} →
  [inst : CategoryTheory.Category.{w', w} 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.toOver F)

If F has a colimit, then the cocone colimit.toOver F with cocone point 𝟙 (colimit F) is also a colimit cocone.

Defined in

Mathlib.CategoryTheory.Limits.Over

Cited by

1 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimit