Theorems · Definition · category theory

CategoryTheory.Limits.Bicones.ext

{J : Type w} →
  {C : Type uC} →
    [inst : CategoryTheory.Category.{uC', uC} C] →
      [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
        {F : J → C} →
          {c c' : CategoryTheory.Limits.Bicone F} →
            (φ : c.pt ≅ c'.pt) →
              autoParam (∀ (j : J), CategoryTheory.CategoryStruct.comp (c.ι j) φ.hom = c'.ι j)
                  CategoryTheory.Limits.Bicones.ext._auto_1 →
                autoParam (∀ (j : J), CategoryTheory.CategoryStruct.comp φ.hom (c'.π j) = c.π j)
                    CategoryTheory.Limits.Bicones.ext._auto_3 →
                  (c ≅ c')

To give an isomorphism between cocones, it suffices to give an isomorphism between their vertices which commutes with the cocone maps.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Biproducts

Cited by

2 results in Mathlib

Foundations

Depth 15 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms