Transporting strict descent of a family through an additive equivalence #
theorem
MagnitudeConjecture.CategoryTheory.ranked_family_of_equivalence
{C : Type u}
[CategoryTheory.Category.{v, u} C]
[CategoryTheory.Preadditive C]
{D : Type u'}
[CategoryTheory.Category.{v', u'} D]
[CategoryTheory.Preadditive D]
(E : C ≌ D)
[E.functor.Additive]
{ι : Type w}
(F : ι → D)
(rank : ι → ℤ)
(hF : ∀ (i j : ι) (f : F i ⟶ F j), f ≠ 0 → ¬CategoryTheory.IsIso f → rank j < rank i)
(i j : ι)
(f : E.inverse.obj (F i) ⟶ E.inverse.obj (F j))
(hf : f ≠ 0)
(hi : ¬CategoryTheory.IsIso f)
:
rank j < rank i
Strict descent of nonzero nonisomorphisms is invariant under an additive equivalence.