Theorems · Definition · category theory

CategoryTheory.Comma.mapRightId

{B : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} B] →
    {A : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} A] →
        {T : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} T] →
            (R : CategoryTheory.Functor B T) →
              (L : CategoryTheory.Functor A T) →
                CategoryTheory.Comma.mapRight L (CategoryTheory.CategoryStruct.id R) ≅
                  CategoryTheory.Functor.id (CategoryTheory.Comma L R)

The functor Comma L R ⥤ Comma L R induced by the identity natural transformation on R is naturally isomorphic to the identity functor.

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