Theorems · Theorem · category theory

CategoryTheory.SingleFunctors.shiftIso_add_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] {A : Type u_5} [inst_2 : AddMonoid A]
  [inst_3 : CategoryTheory.HasShift D A] (F : CategoryTheory.SingleFunctors C D A) (n m a a' a'' : A) (ha' : n + a = a')
  (ha'' : m + a' = a'') (X : C),
  (F.shiftIso (m + n) a a'' ⋯).inv.app X =
    CategoryTheory.CategoryStruct.comp ((F.shiftIso n a a' ha').inv.app X)
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctor D n).map ((F.shiftIso m a' a'' ha'').inv.app X))
        ((CategoryTheory.shiftFunctorAdd D m n).inv.app ((F.functor a'').obj X)))

Defined in

Mathlib.CategoryTheory.Shift.SingleFunctors

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShift