Theorems · Definition · category theory

CategoryTheory.Over.prodLeftIsoPullback

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X : C} →
      (Y Z : CategoryTheory.Over X) →
        [inst_1 : CategoryTheory.Limits.HasPullback Y.hom Z.hom] →
          [inst_2 : CategoryTheory.Limits.HasBinaryProduct Y Z] →
            (Y ⨯ Z).left ≅ CategoryTheory.Limits.pullback Y.hom Z.hom

The product of Y and Z in Over X is isomorphic to Y ×ₓ Z.

Defined in

Mathlib.CategoryTheory.Limits.Constructions.Over.Products

Cited by

8 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasBinaryProduct