Theorems · Theorem · category theory

CategoryTheory.Limits.CatCospanTransform.mkIso_inv_right

∀ {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)
  (left_coherence :
    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)
  (right_coherence :
    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),
  (CategoryTheory.Limits.CatCospanTransform.mkIso left right base left_coherence right_coherence).inv.right = right.inv

Defined in

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

Cited by

1 results in Mathlib

Foundations

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

Assumes

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