Theorems · Theorem · category theory

CategoryTheory.Functor.isoShift_inv_naturality_assoc

∀ {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) {X Y : C} (f : X ⟶ Y) {Z : A}
  (h : F.obj ((CategoryTheory.shiftFunctor C n).obj Y) ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((F.shift n).map f)
      (CategoryTheory.CategoryStruct.comp ((F.isoShift n).inv.app Y) h) =
    CategoryTheory.CategoryStruct.comp ((F.isoShift n).inv.app X)
      (CategoryTheory.CategoryStruct.comp (F.map ((CategoryTheory.shiftFunctor C n).map f)) h)

Defined in

Mathlib.CategoryTheory.Shift.ShiftSequence

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequence