Theorems · Definition · category theory

CategoryTheory.Limits.pullbackProdSndIsoProd

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} →
      (f : X ⟶ Y) →
        (Z : C) →
          [inst_1 : CategoryTheory.Limits.HasBinaryProduct Z Y] →
            [inst_2 : CategoryTheory.Limits.HasBinaryProduct Z X] →
              [inst_3 : CategoryTheory.Limits.HasPullback CategoryTheory.Limits.prod.snd f] →
                CategoryTheory.Limits.pullback CategoryTheory.Limits.prod.snd f ≅ Z ⨯ X

(Z ⨯ Y) ×[Y] X ≅ Z ⨯ X

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

10 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProductCategoryTheory.Limits.HasBinaryProductCategoryTheory.Limits.HasPullback