Theorems · Theorem · category theory

CategoryTheory.SingleFunctors.shiftIso_add

∀ {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] (self : CategoryTheory.SingleFunctors C D A) (n m a a' a'' : A)
  (ha' : n + a = a') (ha'' : m + a' = a''),
  self.shiftIso (m + n) a a'' ⋯ =
    (self.functor a'').isoWhiskerLeft (CategoryTheory.shiftFunctorAdd D m n) ≪≫
      ((self.functor a'').associator (CategoryTheory.shiftFunctor D m) (CategoryTheory.shiftFunctor D n)).symm ≪≫
        CategoryTheory.Functor.isoWhiskerRight (self.shiftIso m a' a'' ha'') (CategoryTheory.shiftFunctor D n) ≪≫
          self.shiftIso n a a' ha'

shiftIso (m + n) is determined by shiftIso m and shiftIso n.

Defined in

Mathlib.CategoryTheory.Shift.SingleFunctors

Cited by

3 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShift