Theorems · Definition · category theory

CategoryTheory.Comma.mapSnd

{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] →
            {B' : Type u₄} →
              [inst_3 : CategoryTheory.Category.{v₄, u₄} B'] →
                {A' : Type u₅} →
                  [inst_4 : CategoryTheory.Category.{v₅, u₅} A'] →
                    {T' : Type u₆} →
                      [inst_5 : CategoryTheory.Category.{v₆, u₆} T'] →
                        {R : CategoryTheory.Functor B T} →
                          {L : CategoryTheory.Functor A T} →
                            {R' : CategoryTheory.Functor B' T'} →
                              {L' : CategoryTheory.Functor A' T'} →
                                {F₂ : CategoryTheory.Functor B B'} →
                                  {F₁ : CategoryTheory.Functor A A'} →
                                    {F : CategoryTheory.Functor T T'} →
                                      (β : F₁.comp L' ⟶ L.comp F) →
                                        (α : R.comp F ⟶ F₂.comp R') →
                                          (CategoryTheory.Comma.map β α).comp (CategoryTheory.Comma.snd L' R') ≅
                                            (CategoryTheory.Comma.snd L R).comp F₂

The isomorphism between map α β ⋙ snd L' R' and snd L R ⋙ F₂, where β : R ⋙ F ⟶ F₂ ⋙ R'.

Defined in

Mathlib.CategoryTheory.Comma.Basic

Cited by

2 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category