For a multi-person (shared) To Do list, can the same categories be shared on each person's list?

Using a shared To Do list with 2 people. Is there a way that 1 person can label with a category and the other person can see it? The categories I place on the shared list do not show on the list of the other individual I share the list with. I know the category comes from my calendar but we share calendar access. I need both of us to be able to see what category each task has been assigned.

If not, is there any other way to organize a to do list except prioritized vs not prioritized?