Theorems · Theorem · category theory

CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_fst

∀ {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.CategoryStruct.comp (CategoryTheory.Limits.diagonalObjPullbackFstIso f g).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Limits.pullback.fst (CategoryTheory.Limits.pullback.fst f g)
          (CategoryTheory.Limits.pullback.fst f g))
        (CategoryTheory.Limits.pullback.fst f g)) =
    CategoryTheory.Limits.pullback.snd (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.snd g g) g) f

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Diagonal

Cited by

2 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks