Theorems · Theorem · category theory

CategoryTheory.Functor.shiftIso_hom_naturality

∀ {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] {X Y : C} (n a a' : M) (ha' : n + a = a')
  (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((F.shift a).map ((CategoryTheory.shiftFunctor C n).map f))
      ((F.shiftIso n a a' ha').hom.app Y) =
    CategoryTheory.CategoryStruct.comp ((F.shiftIso n a a' ha').hom.app X) ((F.shift a').map f)

Defined in

Mathlib.CategoryTheory.Shift.ShiftSequence

Cited by

2 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequence