Theorems · Definition · category theory

CategoryTheory.Over.pullbackComp

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} →
      (f : X ⟶ Y) →
        (g : Y ⟶ Z) →
          [inst_1 : CategoryTheory.Limits.HasPullbacksAlong f] →
            [inst_2 : CategoryTheory.Limits.HasPullbacksAlong g] →
              CategoryTheory.Over.pullback (CategoryTheory.CategoryStruct.comp f g) ≅
                (CategoryTheory.Over.pullback g).comp (CategoryTheory.Over.pullback f)

pullback commutes with composition (up to natural isomorphism).

Defined in

Mathlib.CategoryTheory.Comma.Over.Pullback

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksAlongCategoryTheory.Limits.HasPullbacksAlong