Authors unable to choose category when creating items

Hi there, I've run into a bit of trouble setting up the Author permissions and for the life of me I can't find where it is set in the options or ACL.
The issue is that Authors cannot choose a category for new items if they just hit "+ New Item" on the item listing. The select box is there and not disabled or anything, it is just not populated with any options.

However, if the user first filters by category on the listing page, then clicks +New Item, the item is already set to their chosen category. I am sure I must have turned something off by accident somewhere or something, but I just cannot find it at all.

Would very much appreciate if someone could point me in the right direction!

1 check global ACL in configuration and test
2 check category option in type and test
3 check ACL in category and test

Thanks micker, my issue is more that I can't find the relevant parts in flexi. I have the following global ACL set up for authors, this made the tree available, but even though they show up now, all the category options are disabled. Please see attachment for the global ACL.

When you say to "check category option in type"... In the type configuration I have the following:
'Main category: Allowed subtree' --Blank allows all-- set to blank ("select category")
With Disable subtree parent, this is set to "No".

In the ACL for one of the categories themself (they are all set the same, there is no hidden content section to the site), permissions are all left to inherited for authors.
create
Allowed (Inherited)
delete
Not Allowed (Inherited)
delete own
Allowed (Inherited)
edit
Allowed (Inherited)
edit own
Allowed (Inherited)
edit state
Not Allowed (Inherited)
edit state own
Not Allowed (Inherited)