Theorems · Definition · category theory

CategoryTheory.Comma.mapLeftComp

{A : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} A] →
    {B : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
        {T : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} T] →
            (R : CategoryTheory.Functor B T) →
              {L₁ L₂ L₃ : CategoryTheory.Functor A T} →
                (l : L₁ ⟶ L₂) →
                  (l' : L₂ ⟶ L₃) →
                    CategoryTheory.Comma.mapLeft R (CategoryTheory.CategoryStruct.comp l l') ≅
                      (CategoryTheory.Comma.mapLeft R l').comp (CategoryTheory.Comma.mapLeft R l)

The functor Comma L₁ R ⥤ Comma L₃ R induced by the composition of two natural transformations l : L₁ ⟶ L₂ and l' : L₂ ⟶ L₃ is naturally isomorphic to the composition of the two functors induced by these natural transformations.

Defined in

Mathlib.CategoryTheory.Comma.Basic

Cited by

4 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category