Theorems · Definition · category theory

CategoryTheory.Comma.mapFst

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

The isomorphism between map α β ⋙ fst L' R' and fst L R ⋙ F₁, where α : F₁ ⋙ L' ⟶ L ⋙ F.

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