Theorems · Definition · category theory

CategoryTheory.Limits.isColimitOfIsColimitCofanMkObj

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (G : CategoryTheory.Functor C D) →
          {J : Type w} →
            (f : J → C) →
              [CategoryTheory.Limits.ReflectsColimit (CategoryTheory.Discrete.functor f) G] →
                {P : C} →
                  (g : (j : J) → f j ⟶ P) →
                    CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.Cofan.mk (G.obj P) fun j => G.map (g j)) →
                      CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.Cofan.mk P g)

The property of reflecting coproducts expressed in terms of cofans.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.ReflectsColimit