Theorems · Theorem · category theory

CategoryTheory.Functor.shiftIso_add_hom_app

∀ {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 a a' a'' : M) (ha' : n + a = a')
  (ha'' : m + a' = a'') (X : C),
  (F.shiftIso (m + n) a a'' ⋯).hom.app X =
    CategoryTheory.CategoryStruct.comp ((F.shift a).map ((CategoryTheory.shiftFunctorAdd C m n).hom.app X))
      (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))

Defined in

Mathlib.CategoryTheory.Shift.ShiftSequence

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequence