Theorems · Theorem · category theory

CategoryTheory.Limits.pullback_lift_diagonal_isPullback

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X Y : C} [inst_1 : CategoryTheory.Limits.HasPullbacks C]
  {S : C} (g : Y ⟶ X) (f : X ⟶ S),
  CategoryTheory.IsPullback g (CategoryTheory.Limits.pullback.lift (CategoryTheory.CategoryStruct.id Y) g ⋯)
    (CategoryTheory.Limits.pullback.diagonal f)
    (CategoryTheory.Limits.pullback.map (CategoryTheory.CategoryStruct.comp g f) f f f g
      (CategoryTheory.CategoryStruct.id X) (CategoryTheory.CategoryStruct.id S) ⋯ ⋯)

Informally, this is a special case of pullback_map_diagonal_isPullback for T = X.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Diagonal

Cited by

1 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks