Theorems · Definition · category theory

CategoryTheory.Limits.CatCospanTransform.mkIso

{A : Type u₁} →
  {B : Type u₂} →
    {C : Type u₃} →
      {A' : Type u₄} →
        {B' : Type u₅} →
          {C' : Type u₆} →
            [inst : CategoryTheory.Category.{v₁, u₁} A] →
              [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
                [inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
                  {F : CategoryTheory.Functor A B} →
                    {G : CategoryTheory.Functor C B} →
                      [inst_3 : CategoryTheory.Category.{v₄, u₄} A'] →
                        [inst_4 : CategoryTheory.Category.{v₅, u₅} B'] →
                          [inst_5 : CategoryTheory.Category.{v₆, u₆} C'] →
                            {F' : CategoryTheory.Functor A' B'} →
                              {G' : CategoryTheory.Functor C' B'} →
                                {ψ ψ' : CategoryTheory.Limits.CatCospanTransform F G F' G'} →
                                  (left : ψ.left ≅ ψ'.left) →
                                    (right : ψ.right ≅ ψ'.right) →
                                      (base : ψ.base ≅ ψ'.base) →
                                        autoParam
                                            (CategoryTheory.CategoryStruct.comp
                                                (CategoryTheory.CatCommSq.iso F ψ.left ψ.base F').hom
                                                (CategoryTheory.Functor.whiskerRight left.hom F') =
                                              CategoryTheory.CategoryStruct.comp (F.whiskerLeft base.hom)
                                                (CategoryTheory.CatCommSq.iso F ψ'.left ψ'.base F').hom)
                                            CategoryTheory.Limits.CatCospanTransform.mkIso._auto_1 →
                                          autoParam
                                              (CategoryTheory.CategoryStruct.comp
                                                  (CategoryTheory.CatCommSq.iso G ψ.right ψ.base G').hom
                                                  (CategoryTheory.Functor.whiskerRight right.hom G') =
                                                CategoryTheory.CategoryStruct.comp (G.whiskerLeft base.hom)
                                                  (CategoryTheory.CatCommSq.iso G ψ'.right ψ'.base G').hom)
                                              CategoryTheory.Limits.CatCospanTransform.mkIso._auto_3 →
                                            (ψ ≅ ψ')

A constructor for isomorphisms of CatCospanTransform's.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform

Cited by

8 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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