Theorems · Definition · category theory

CategoryTheory.liftsToColimitOfCreates

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {J : Type w} →
          [inst_2 : CategoryTheory.Category.{w', w} J] →
            (K : CategoryTheory.Functor J C) →
              (F : CategoryTheory.Functor C D) →
                [CategoryTheory.CreatesColimit K F] →
                  (c : CategoryTheory.Limits.Cocone (K.comp F)) →
                    (t : CategoryTheory.Limits.IsColimit c) → CategoryTheory.LiftsToColimit K F c t

If F creates the colimit of K, any cocone lifts to a colimit.

Defined in

Mathlib.CategoryTheory.Limits.Creates

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CreatesColimit