I know that CNN(conv-neural-network) could classify more than 10 thousands of images of the ImageNet.
I find that CNN could only classify 10-20 text classes as this paper write.
How many classes can CNN classify the short text? What is the high limit of the classes number?
The number of categories a classifier could classify with good precision/recall is decided by (but not limited to):
It's hard to just give you a number without knowing the answers to above questions.