Theorems · Theorem · category theory

CategoryTheory.shiftFunctorAdd_assoc

∀ (C : Type u) {A : Type u_1} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : AddMonoid A]
  [inst_2 : CategoryTheory.HasShift C A] (a₁ a₂ a₃ : A),
  CategoryTheory.shiftFunctorAdd C (a₁ + a₂) a₃ ≪≫
      CategoryTheory.Functor.isoWhiskerRight (CategoryTheory.shiftFunctorAdd C a₁ a₂)
          (CategoryTheory.shiftFunctor C a₃) ≪≫
        (CategoryTheory.shiftFunctor C a₁).associator (CategoryTheory.shiftFunctor C a₂)
          (CategoryTheory.shiftFunctor C a₃) =
    CategoryTheory.shiftFunctorAdd' C a₁ (a₂ + a₃) (a₁ + a₂ + a₃) ⋯ ≪≫
      (CategoryTheory.shiftFunctor C a₁).isoWhiskerLeft (CategoryTheory.shiftFunctorAdd C a₂ a₃)

Defined in

Mathlib.CategoryTheory.Shift.Basic

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAddMonoidCategoryTheory.HasShift