Equivalence of Hom-finite tensor categories and tensor categories

Determine whether every Hom-finite tensor category is a tensor category, equivalently, whether the inclusion of tensor categories into ind-tensor categories is strict.

Background

The appendix distinguishes artinian tensor categories, Hom-finite tensor categories, tensor categories, and ind-tensor categories. The authors construct a Hom-finite symmetric tensor category with objects of infinite length, showing that the first inclusion is strict.

They explicitly state that it remains unresolved whether the inclusion from tensor categories to ind-tensor categories is strict.