Theorems · Definition · category theory

CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.mkIso

{A : Type u₁} →
  {B : Type u₂} →
    {C : Type u₃} →
      [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} →
                {X : Type u₄} →
                  [inst_3 : CategoryTheory.Category.{v₄, u₄} X] →
                    {S S' : CategoryTheory.Limits.CategoricalPullback.CatCommSqOver F G X} →
                      (eₗ : S.fst ≅ S'.fst) →
                        (eᵣ : S.snd ≅ S'.snd) →
                          autoParam
                              (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.whiskerRight eₗ.hom F)
                                  S'.iso.hom =
                                CategoryTheory.CategoryStruct.comp S.iso.hom
                                  (CategoryTheory.Functor.whiskerRight eᵣ.hom G))
                              CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.mkIso._auto_1 →
                            (S ≅ S')

A constructor for isomorphisms in CatCommSqOver

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic

Cited by

7 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category