Theorems · Theorem · category theory

CategoryTheory.NatTrans.app_shift_assoc

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {F₁ F₂ : CategoryTheory.Functor C D} (τ : F₁ ⟶ F₂) {A : Type u_5}
  [inst_2 : AddMonoid A] [inst_3 : CategoryTheory.HasShift C A] [inst_4 : CategoryTheory.HasShift D A]
  [inst_5 : F₁.CommShift A] [inst_6 : F₂.CommShift A] [CategoryTheory.NatTrans.CommShift τ A] (a : A) (X : C) {Z : D}
  (h : F₂.obj ((CategoryTheory.shiftFunctor C a).obj X) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (τ.app ((CategoryTheory.shiftFunctor C a).obj X)) h =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.commShiftIso F₁ a).hom.app X)
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctor D a).map (τ.app X))
        (CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.commShiftIso F₂ a).inv.app X) h))

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.Functor.CommShiftCategoryTheory.NatTrans.CommShift