There are two places to see climb categories on Ride with GPS currently, when viewing any route/ride or when looking at a segment that is a climb.
Climb categories on segments
If a segment is a climb, we will automatically display the climb category as well as the FIETS index in the top left of the segment view page. For an example, we can look at the McBeth Hillclimb in Eugene, Oregon. Here is a screenshot of the top left box that shows the climb category: