Theorems · Theorem · category theory

CategoryTheory.Functor.commShiftIso_hom_naturality

∀ {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] (F : CategoryTheory.Functor C D) {A : Type u_4} [inst_2 : AddMonoid A]
  [inst_3 : CategoryTheory.HasShift C A] [inst_4 : CategoryTheory.HasShift D A] [inst_5 : F.CommShift A] {X Y : C}
  (f : X ⟶ Y) (a : A),
  CategoryTheory.CategoryStruct.comp (F.map ((CategoryTheory.shiftFunctor C a).map f))
      ((CategoryTheory.Functor.commShiftIso F a).hom.app Y) =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.commShiftIso F a).hom.app X)
      ((CategoryTheory.shiftFunctor D a).map (F.map f))

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

5 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShift