I have a data set that contains the columns Date, Cat, and QTY. What I want to do is add a unique column that only counts unique Cat values when it does the row count. This is what I want my result set to look like:

By using the SQL query below, I'm able to get row using the row_number() function.
However, I can't get that unique column that I have depicted above. When I add group by to the OVER clause, it does not work. Does anybody have any ideas as how I could get this unique count column to work?
SELECT
Date,
ROW_NUMBER() OVER (PARTITION BY Date ORDER By Date, Cat) as ROW,
Cat,
Qty
FROM SOURCE