We give results and observations which allow the application of the logarithmic tensor category theory of Lepowsky, Zhang and the author ([HLZ1]-[HLZ9]) to more general vertex (operator) algebras and their module categories than those studied in a paper by the author ([H2]).

These remarks are based on the authors' answers to questions asked by Antun Milas. I am very grateful for him for the questions and discussions. I would also like to thank James Lepowsky for helpful comments.