If you want to limit a user to a single category, then this is not possible through the Joomla backend.

You will have to enable frontend editing in K2, then create a K2 user group in which you'll assign this specific user.

In the K2 User Group, make sure to select the right editing permissions and assign access only to that single category.

Finally, publish the K2 User module in some module position so the user can login and see the option to add new content from that module.