Theorems · Definition · category theory

CategoryTheory.ChosenPullbacksAlong.lift

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {Y Z X : C} →
      {f : Y ⟶ X} →
        {g : Z ⟶ X} →
          [inst_1 : CategoryTheory.ChosenPullbacksAlong g] →
            {W : C} →
              (a : W ⟶ Y) →
                (b : W ⟶ Z) →
                  autoParam (CategoryTheory.CategoryStruct.comp a f = CategoryTheory.CategoryStruct.comp b g)
                      _auto_75✝ →
                    (W ⟶ CategoryTheory.ChosenPullbacksAlong.pullbackObj f g)

Given morphisms a : W ⟶ Y and b : W ⟶ Z satisfying a ≫ f = b ≫ g, constructs the unique morphism W ⟶ pullbackObj f g which lifts a and b.

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong

Cited by

8 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacksAlong