∀ {ι : Type u_1} {ι' : Type u_2} {c : ComplexShape ι} {c' : ComplexShape ι'} {C : Type u_3} {D : Type u_4}
  [inst : CategoryTheory.Category.{v_1, u_3} C] [inst_1 : CategoryTheory.Category.{v_2, u_4} D]
  [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D]
  (K : HomologicalComplex C c') (F : CategoryTheory.Functor C D) [inst_4 : F.PreservesZeroMorphisms]
  (e : c.Embedding c') [K.IsStrictlySupported e], ((F.mapHomologicalComplex c').obj K).IsStrictlySupported e