Theorems · Theorem · category theory

CategoryTheory.Join.mapWhiskerLeft_associator_hom_assoc

∀ (A : Type u_1) {B : Type u_2} {C : Type u_3} {D : Type u_4} [inst : CategoryTheory.Category.{v_1, u_1} A]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} B] [inst_2 : CategoryTheory.Category.{v_3, u_3} C]
  [inst_3 : CategoryTheory.Category.{v_4, u_4} D] {E : Type u_5} [inst_4 : CategoryTheory.Category.{v_5, u_5} E]
  (F : CategoryTheory.Functor B C) (G : CategoryTheory.Functor C D) (H : CategoryTheory.Functor D E)
  {Z : CategoryTheory.Functor (CategoryTheory.Join A B) (CategoryTheory.Join A E)}
  (h : CategoryTheory.Join.mapPair (CategoryTheory.Functor.id A) (F.comp (G.comp H)) ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Join.mapWhiskerLeft (CategoryTheory.Functor.id A) (F.associator G H).hom) h =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Join.mapCompRight A (F.comp G) H).hom
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Functor.whiskerRight (CategoryTheory.Join.mapCompRight A F G).hom
          (CategoryTheory.Join.mapPair (CategoryTheory.Functor.id A) H))
        (CategoryTheory.CategoryStruct.comp
          ((CategoryTheory.Join.mapPair (CategoryTheory.Functor.id A) F).associator
              (CategoryTheory.Join.mapPair (CategoryTheory.Functor.id A) G)
              (CategoryTheory.Join.mapPair (CategoryTheory.Functor.id A) H)).hom
          (CategoryTheory.CategoryStruct.comp
            ((CategoryTheory.Join.mapPair (CategoryTheory.Functor.id A) F).whiskerLeft
              (CategoryTheory.Join.mapCompRight A G H).inv)
            (CategoryTheory.CategoryStruct.comp (CategoryTheory.Join.mapCompRight A F (G.comp H)).inv h))))

Defined in

Mathlib.CategoryTheory.Join.Pseudofunctor

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category