Theorems · Definition · category theory

CategoryTheory.Limits.spanExt

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z X' Y' Z' : C} →
      (iX : X ≅ X') →
        (iY : Y ≅ Y') →
          (iZ : Z ≅ Z') →
            {f : X ⟶ Y} →
              {g : X ⟶ Z} →
                {f' : X' ⟶ Y'} →
                  {g' : X' ⟶ Z'} →
                    CategoryTheory.CategoryStruct.comp iX.hom f' = CategoryTheory.CategoryStruct.comp f iY.hom →
                      CategoryTheory.CategoryStruct.comp iX.hom g' = CategoryTheory.CategoryStruct.comp g iZ.hom →
                        (CategoryTheory.Limits.span f g ≅ CategoryTheory.Limits.span f' g')

Construct an isomorphism of spans from components.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan

Cited by

27 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category