Theorems · Definition · category theory

CategoryTheory.Limits.isColimitOfReflectsOfMapIsColimit

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (G : CategoryTheory.Functor C D) →
          {P X Y : C} →
            (f : X ⟶ P) →
              (g : Y ⟶ P) →
                [CategoryTheory.Limits.ReflectsColimit (CategoryTheory.Limits.pair X Y) G] →
                  CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.BinaryCofan.mk (G.map f) (G.map g)) →
                    CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.BinaryCofan.mk f g)

The property of reflecting coproducts expressed in terms of binary cofans.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.ReflectsColimit