Theorems · Definition · category theory

CategoryTheory.IsPullback.isoPullback

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

Any object at the top left of a pullback square is isomorphic to the pullback provided by the HasLimit API.

Defined in

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

Cited by

42 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullback