Theorems · Definition · category theory

CategoryTheory.ChosenPullbacksAlong.pullbackComp

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y Z : C} →
      (f : X ⟶ Y) →
        (g : Y ⟶ Z) →
          [inst_1 : CategoryTheory.ChosenPullbacksAlong f] →
            [inst_2 : CategoryTheory.ChosenPullbacksAlong g] →
              [inst_3 : CategoryTheory.ChosenPullbacksAlong (CategoryTheory.CategoryStruct.comp f g)] →
                CategoryTheory.ChosenPullbacksAlong.pullback (CategoryTheory.CategoryStruct.comp f g) ≅
                  (CategoryTheory.ChosenPullbacksAlong.pullback g).comp (CategoryTheory.ChosenPullbacksAlong.pullback f)

Any chosen pullback of a composite of morphisms is naturally isomorphic to the composition of chosen pullback functors.

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong

Cited by

4 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacksAlongCategoryTheory.ChosenPullbacksAlongCategoryTheory.ChosenPullbacksAlong