Theorems · Theorem · category theory

CategoryTheory.Functor.shiftIso_hom_app_comp

∀ {C : Type u_1} {A : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_3, u_3} A] (F : CategoryTheory.Functor C A) {M : Type u_4} [inst_2 : AddMonoid M]
  [inst_3 : CategoryTheory.HasShift C M] [inst_4 : F.ShiftSequence M] (n m mn : M) (hnm : m + n = mn) (a a' a'' : M)
  (ha' : n + a = a') (ha'' : m + a' = a'') (X : C),
  CategoryTheory.CategoryStruct.comp ((F.shiftIso n a a' ha').hom.app ((CategoryTheory.shiftFunctor C m).obj X))
      ((F.shiftIso m a' a'' ha'').hom.app X) =
    CategoryTheory.CategoryStruct.comp ((F.shift a).map ((CategoryTheory.shiftFunctorAdd' C m n mn hnm).inv.app X))
      ((F.shiftIso mn a a'' ⋯).hom.app X)

Defined in

Mathlib.CategoryTheory.Shift.ShiftSequence

Cited by

1 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequence