Theorems · Theorem · category theory

CategoryTheory.Functor.CommShift.isoAdd_inv_app

∀ {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] {F : CategoryTheory.Functor C D} {A : Type u_4} [inst_2 : AddMonoid A]
  [inst_3 : CategoryTheory.HasShift C A] [inst_4 : CategoryTheory.HasShift D A] {a b : A}
  (e₁ : (CategoryTheory.shiftFunctor C a).comp F ≅ F.comp (CategoryTheory.shiftFunctor D a))
  (e₂ : (CategoryTheory.shiftFunctor C b).comp F ≅ F.comp (CategoryTheory.shiftFunctor D b)) (X : C),
  (CategoryTheory.Functor.CommShift.isoAdd e₁ e₂).inv.app X =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctorAdd D a b).hom.app (F.obj X))
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctor D b).map (e₁.inv.app X))
        (CategoryTheory.CategoryStruct.comp (e₂.inv.app ((CategoryTheory.shiftFunctor C a).obj X))
          (F.map ((CategoryTheory.shiftFunctorAdd C a b).inv.app X))))

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShift