Theorems · Theorem · category theory

CategoryTheory.IsPullback.of_hasPullback

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y Z : C} (f : X ⟶ Z) (g : Y ⟶ Z)
  [inst_1 : CategoryTheory.Limits.HasPullback f g],
  CategoryTheory.IsPullback (CategoryTheory.Limits.pullback.fst f g) (CategoryTheory.Limits.pullback.snd f g) f g

The pullback provided by HasPullback f g fits into an IsPullback.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs

Cited by

70 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullback