Theorems · Definition · category theory

CategoryTheory.Limits.diagonalObjPullbackFstIso

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasPullbacks C] →
      {X Y Z : C} →
        (f : X ⟶ Z) →
          (g : Y ⟶ Z) →
            CategoryTheory.Limits.pullback.diagonalObj (CategoryTheory.Limits.pullback.fst f g) ≅
              CategoryTheory.Limits.pullback
                (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.snd g g) g) f

The diagonal object of X ×[Z] Y ⟶ X is isomorphic to Δ_{Y/Z} ×[Z] X.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Diagonal

Cited by

15 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks