Theorems · Theorem · category theory

CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app_assoc

∀ {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 : A) {Z : B'}
  (h : F'.obj (ψ'.left.obj x) ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.CatCommSq.iso F ψ.left ψ.base F').hom.app x)
      (CategoryTheory.CategoryStruct.comp (F'.map (α.left.app x)) h) =
    CategoryTheory.CategoryStruct.comp (α.base.app (F.obj x))
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.CatCommSq.iso F ψ'.left ψ'.base F').hom.app x) h)

Defined in

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

Cited by

0 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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