Theorems · Definition · category theory

CategoryTheory.Limits.pullbackRightPullbackFstIso

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

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

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting

Cited by

43 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasPullback