Theorems · Definition · category theory

CategoryTheory.Limits.createsColimitOfOp

{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.CreatesLimit K.op F.op] → CategoryTheory.CreatesColimit K F

If F.op : Cᵒᵖ ⥤ Dᵒᵖ creates limits of K.op : Jᵒᵖ ⥤ Cᵒᵖ, then F : C ⥤ D creates colimits of K : J ⥤ C.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Creates.Opposites

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CreatesLimit