Theorems · Theorem · category theory

CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app

∀ {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'} (α : ψ ⟶ ψ') (x : C),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.CatCommSq.iso G ψ.right ψ.base G').hom.app x)
      (G'.map (α.right.app x)) =
    CategoryTheory.CategoryStruct.comp (α.base.app (G.obj x))
      ((CategoryTheory.CatCommSq.iso G ψ'.right ψ'.base G').hom.app x)

Defined in

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

Cited by

1 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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