Theorems · Definition · category theory

CategoryTheory.Limits.pullbackProdFstIsoProd

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

X ×[Y] (Y ⨯ Z) ≅ X ⨯ Z

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

12 results in Mathlib

Foundations

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

Assumes

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