Theorems · Definition · category theory

CategoryTheory.Limits.IsColimit.underPost

{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] →
        {D : CategoryTheory.Functor J C} →
          {c : CategoryTheory.Limits.Cocone D} →
            CategoryTheory.Limits.IsColimit c →
              (j : J) → [(CategoryTheory.Under.forget j).Final] → CategoryTheory.Limits.IsColimit (c.underPost j)

If Over j ⥤ J is final, restricting a colimit cocone to the diagram below j, preserves the limit.

Defined in

Mathlib.CategoryTheory.Limits.Final

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.Final