Theorems · Definition · category theory

CategoryTheory.IsPullback.isoOverPullback

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

An IsPullback square yields an isomorphism Over.mk fst ≅ Over.mk (pullback.fst f g) in Over X.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

Cited by

4 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksAlong