Theorems · Theorem · category theory

CategoryTheory.Functor.FullyFaithful.hasShift.map_add_hom_app

∀ {C : Type u} {A : Type u_1} [inst : CategoryTheory.Category.{v, u} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{v_1, u_2} D] [inst_2 : AddMonoid A] [inst_3 : CategoryTheory.HasShift D A]
  {F : CategoryTheory.Functor C D} (hF : F.FullyFaithful) (s : A → CategoryTheory.Functor C C)
  (i : (i : A) → (s i).comp F ≅ F.comp (CategoryTheory.shiftFunctor D i)) (a b : A) (X : C),
  F.map ((CategoryTheory.Functor.FullyFaithful.hasShift.add hF s i a b).hom.app X) =
    CategoryTheory.CategoryStruct.comp ((i (a + b)).hom.app X)
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctorAdd D a b).hom.app (F.obj X))
        (CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctor D b).map ((i a).inv.app X))
          ((i b).inv.app ((s a).obj X))))

Defined in

Mathlib.CategoryTheory.Shift.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShift