Theorems · Definition · category theory

CategoryTheory.MonoOver.pullbackComp

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

pullback commutes with composition (up to a natural isomorphism)

Defined in

Mathlib.CategoryTheory.Subobject.MonoOver

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks