Theorems · Definition · category theory

CategoryTheory.Limits.pullbackLeftPullbackSndIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {W X Y Z : C} →
      (f : X ⟶ Z) →
        (g : Y ⟶ Z) →
          (g' : W ⟶ Y) →
            [inst_1 : CategoryTheory.Limits.HasPullback f g] →
              [inst_2 : CategoryTheory.Limits.HasPullback (CategoryTheory.Limits.pullback.snd f g) g'] →
                CategoryTheory.Limits.pullback (CategoryTheory.Limits.pullback.snd f g) g' ≅
                  CategoryTheory.Limits.pullback f (CategoryTheory.CategoryStruct.comp g' g)

The canonical isomorphism (X ×[Z] Y) ×[Y] W ≅ X ×[Z] W

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting

Cited by

19 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasPullback