Theorems · Theorem · category theory

CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.mkIso_hom_fst

∀ {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)
  (w :
    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),
  (CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.mkIso eₗ eᵣ w).hom.fst = eₗ.hom

Defined in

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

Cited by

1 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category