How can I get a running total of submissions per category?

It seems to me that you mean you want to figure out and total up how many submissions you have for each of your received form submissions.

The best way I can think of to do something of this sort would be to create a visual report.

Doing this would make it so that it is displayed via graphs for each of your categories so that you can see at a glance the totaled submissions for your categories in real-time as they are received.

Here's a demo form: https://form.jotform.com/60684550905964    [clone me!]

Here's the demo form's visual report (chart): https://www.jotform.com/report/60684443220046 

You'll notice that it's charting the categories I set for 3 received test submissions.