Yes, a Senior Supervisor must be a Category Supervisor.
(See the Related question.)
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The only thing a Category Supervisor has that a Floating Supervisor does not is something on their profile that says the category(ies) they supervise, the category supervisor badge, and their...
If a floating supervisor wishes to become a category supervisor, they can apply in the same way that a non-supervisor would, by sending an email to the appropriate email address.