Is there a Chinese WordNet? WordNet is a database of English words, which includes semantic relationships of words too.  It includes synonym and antonym-relationships, as well as "categories".  For example, it will tell me that a tabby is a cat and that a cat is an animal.

Is there anything comparable for Chinese, which is freely downloadable?

Anything that can be used online is already useful, but I'd prefer a database that I can download and analyse on my own computer.  I only need it for personal use (in case the license doesn't allow anything else).
For the Simplified Chinese script, there is Chinese Open Wordnet which you can search online.

This is part of Open Multilingual Wordnet, which also links to a smaller project called Chinese WordNet which was produced in Taiwan in 2010 and uses the Traditional Chinese script.  That one also has a 2012 version called Chinese WordNet 2, but the license of Chinese WordNet 2 is much more restrictive than that of the original Chinese WordNet or Chinese Open Wordnet.  Chinese WordNet 2 is non-commercial use only and no redistribution without permission, which means others have not integrated it with their online query systems and such.  You can still download it if you don't mind doing a bit of programming to read out the data (I suggest use the "CWN DataBase" link and the output.sqlite file; if you want to process it as text do echo .dump|sqlite3 output.sqlite &gt; output.txt on GNU/Linux).

However if you can convert your input to the Simplified Chinese script then you might as well just use Chinese Open Wordnet.