Theorems · Theorem · category theory

CategoryTheory.Join.mapWhiskerLeft_whiskerLeft

∀ (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] (F : CategoryTheory.Functor B C) {G H : CategoryTheory.Functor C D}
  (η : G ⟶ H),
  CategoryTheory.Join.mapWhiskerLeft (CategoryTheory.Functor.id A) (F.whiskerLeft η) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Join.mapCompRight A F G).hom
      (CategoryTheory.CategoryStruct.comp
        ((CategoryTheory.Join.mapPair (CategoryTheory.Functor.id A) F).whiskerLeft
          (CategoryTheory.Join.mapWhiskerLeft (CategoryTheory.Functor.id A) η))
        (CategoryTheory.Join.mapCompRight A F H).inv)

Defined in

Mathlib.CategoryTheory.Join.Pseudofunctor

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category