Yes a user can set a category as his favorite .
After openning a category question there will be button at the right side top of the main area . see the screen shot
If you need this side of the Categories in the http://www.your-site.org/categories , then you might need to write a plugin or do some core hacks .
Hope this helps .
Welcome to the Q&A site for Question2Answer.
If you have a question about Q2A, please ask here, in English.
To report a bug, please create a new issue on Github or ask a question here with the bug tag.
If you just want to try Q2A, please use the demo site.