This was found when working on KYLO-618.
The 'Administer Categories' permission should allow a user to go to Admin->Properties and set 'Category Fields' information. However, this permission alone is not sufficient as noted in KYLO-618. The 'Access Feeds' permission is also required for setting the 'Category Fields'. This is somewhat non-intuitive since 'Administer Categories' should be able to hold on its own as it's name suggests.
A mechanism to de-couple the two permissions, or auto-grant 'Access Feeds' when 'Administer Categories' is given, must be devised.