Theorems · Theorem · category theory

CategoryTheory.Functor.shiftIso_add

∀ {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''),
  F.shiftIso (m + n) a a'' ⋯ =
    CategoryTheory.Functor.isoWhiskerRight (CategoryTheory.shiftFunctorAdd C m n) (F.shift a) ≪≫
      (CategoryTheory.shiftFunctor C m).associator (CategoryTheory.shiftFunctor C n) (F.shift a) ≪≫
        (CategoryTheory.shiftFunctor C m).isoWhiskerLeft (F.shiftIso n a a' ha') ≪≫ F.shiftIso m a' a'' ha''

Defined in

Mathlib.CategoryTheory.Shift.ShiftSequence

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequence