Theorems · Definition · category theory

CategoryTheory.MonoOver.liftComp

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {X Z : C} →
          {Y : D} →
            (F : CategoryTheory.Functor (CategoryTheory.Over X) (CategoryTheory.Over Y)) →
              (G : CategoryTheory.Functor (CategoryTheory.Over Y) (CategoryTheory.Over Z)) →
                (h₁ :
                    ∀ (f : CategoryTheory.MonoOver X),
                      CategoryTheory.Mono (F.obj ((CategoryTheory.MonoOver.forget X).obj f)).hom) →
                  (h₂ :
                      ∀ (f : CategoryTheory.MonoOver Y),
                        CategoryTheory.Mono (G.obj ((CategoryTheory.MonoOver.forget Y).obj f)).hom) →
                    (CategoryTheory.MonoOver.lift F h₁).comp (CategoryTheory.MonoOver.lift G h₂) ≅
                      CategoryTheory.MonoOver.lift (F.comp G) ⋯

MonoOver.lift commutes with composition of functors.

Defined in

Mathlib.CategoryTheory.Subobject.MonoOver

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category