Although as Tim said there's no perfect way to do that, let me point out three things that may be helpful.
There are a couple of different reports in mod/quiz/report/. You could probably use one of them as a starting point to author a new report with the information you want.
We are planning to achieve the same goal by using different vocabulary. We create a Topic with several Quizzes, but treat the category as one quiz and each Quiz as a subsection. Each section covers one category. In Gradebook, we'll create a calculated grade for the entire "quiz", which is actually a Topic. In the end, that gives grades for each subsection as well as a combined grade.
Tim posted that OU is planning to implement subsections within quizzes, though initially without grading the subsections. The response indicated many people would like subsections to be graded, so that will feature will probably be added in the not-too-distant future, and you could help make that happen. One could have each subsection cover a category and achieve your goal.