Akeeba Ticket System uses Joomla's category manager for its tickets categories. That is to say, the ticket categories are managed by Joomla's com_categories, just like Joomla's own article categories.
One of the main features of Joomla's category manager is the support for nested categories. One category can be under a parent category which is under a grandparent category and so on.
In most cases you are not going to use nested categories for tickets. Typically, you will only have a small handful of ticket categories. Larger organisations with thousands of clients and dozens of support staff may need to use nested categories to make it easier for clients to locate the support category they need and for the staff to provide support.
If you are using nested categories the same considerations apply as with any other Joomla component, core or third party, which has nested categories.
Permissions are cascaded across categories first, then by user groups. When Joomla encounters an explicit Deny on any given permission throughout the category and user groups cascade it will be denying that privilege even if a child category and/or other user group has an explicit Allow for the same permissions. The rule is simple: Deny is stronger than Allow which is stronger than Inherit. We recommend using a third party extension to understand how permissions cascade across categories and user groups on your site.
Access levels do not cascade but may make it impossible to reach a category. If the parent category has its Access set to Special and the child category has its access set to Public then a Registered user can only access the child category but not the parent category. Normally, the user would need to go into the parent category to navigate into the child category. Therefore you are making it hard (but NOT impossible!) for a user to navigate into the child category. Do note that a user could enter the URL to the child category directly to access it. Therefore setting the Access of a parent category does NOT protect children categories from being accessed.
Conversely, if you want to allow easy access to the child
category you should create a menu item to that category. Otherwise
your user would need to know the child category's alias and understand
how Joomla URL routing works to construct a URL similar to
https://www.example.com/tickets/parent/child.html to view
the child category.
Some category options have a Use Global option value. When you select that special option value you are telling Joomla to use the value from the parent category. If the parent category does not have a value it will keep searching until it finds the root category. If it hits the root category it will fall back to the setting you specified for that option in the component's Options page. We recommend setting all options to explicit values (Show / Hide, Yes / No, ...) to avoid any misunderstandings about what Joomla and ATS do when trying to determine which is the actual option value they need to use for a Use Global option value.