"in three categories" is correct and can be used in written English.
For example: "The items were divided into three categories based on their size."
He placed these in three categories.
For now, Blue Origin's business plans fall in three categories.
They fit in three categories: medicine, money and memory.
Federal officials said the Investing in Innovation Fund would be distributed in three categories.
The restaurants are marked in three categories and given a star rating from zero to five.
Every year, Breakthrough Prizes are awarded in three categories: life sciences, fundamental physics, and math.
Prizes are offered in three categories: 14-and-under, 18-and-under and open.
As far as Maluszynski can tell, Vegas carpets come in three categories.
Mr. Woo was a Pulitzer Prize finalist in three categories: national reporting, foreign correspondence and commentary.
The prizes are in three categories: marlin; tuna, dolphin and wahoo; and catch-and-release.
They've studied a total of 38 human-factor variables in three categories.
