Theorems · Theorem · category theory

CategoryTheory.SingleFunctors.isoMk_inv_hom

∀ {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] {F G : CategoryTheory.SingleFunctors C D A}
  (iso : (a : A) → F.functor a ≅ G.functor a)
  (comm :
    ∀ (n a a' : A) (ha' : n + a = a'),
      CategoryTheory.CategoryStruct.comp (F.shiftIso n a a' ha').hom (iso a).hom =
        CategoryTheory.CategoryStruct.comp
          (CategoryTheory.Functor.whiskerRight (iso a').hom (CategoryTheory.shiftFunctor D n))
          (G.shiftIso n a a' ha').hom)
  (a : A), (CategoryTheory.SingleFunctors.isoMk iso comm).inv.hom a = (iso a).inv

Defined in

Mathlib.CategoryTheory.Shift.SingleFunctors

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShift