'what categories of' is correct and usable in written English.
It can be used to ask a question about types or categories of something. For example, "What categories of books do you like to read?".
What categories of people might fix computers in elections?
Among the questions they are wrestling with are these: What categories of crimes should it cover?
What categories of images are documentary and what kinds are not?
By the way, Pew asked similar questions about what categories of government spending to cut in 2011.
The coroner, Judge Nicholas Hilliard QC, reconvened the hearing on 18 December with a brief public hearing before going into closed session to discuss what categories of information could be covered by the PII certificate.
In his De jure belli ac pacis (1625; On the Law of War and Peace, Hugo Grotiuss took note of a long-standing controversy in regard to what categories of cargo might be confiscated in the same way as weapons.
It is not known what category of offences are covered.
But Martin Chamberlain QC, for the justice secretary, Chris Grayling, said it depended what category of death was being considered.
She said she had never asked the journalist to name the source, nor had she asked what category of person it was.
But how that information can be used and from what category of sex offender it is collected varies according to the states' laws, experts said.
And for those who still think that even more austerity is somehow the road to recovery, the question has to be, what category of spending, exactly, do you expect to rise?
