Theorems · Definition · category theory

CategoryTheory.Limits.pullbackZeroZeroIso

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroObject C] →
      [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
        (X Y : C) → [inst_3 : CategoryTheory.Limits.HasBinaryProduct X Y] → CategoryTheory.Limits.pullback 0 0 ≅ X ⨯ Y

The pullback over the zero object is the product.

Defined in

Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects

Cited by

5 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryProduct