Theorems · Definition · category theory

CategoryTheory.Comma.preLeftIso

{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] →
            {C : Type u₄} →
              [inst_3 : CategoryTheory.Category.{v₄, u₄} C] →
                (F : CategoryTheory.Functor C A) →
                  (L : CategoryTheory.Functor A T) →
                    (R : CategoryTheory.Functor B T) →
                      CategoryTheory.Comma.preLeft F L R ≅
                        CategoryTheory.Comma.map (F.comp L).rightUnitor.inv
                          (CategoryTheory.CategoryStruct.comp R.rightUnitor.hom R.leftUnitor.inv)

Comma.preLeft is a particular case of Comma.map, but with better definitional properties.

Defined in

Mathlib.CategoryTheory.Comma.Basic

Cited by

0 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category