Are there any intersections between Theory A and Theory B? In the following two questions Origins and applications of Theory A vs Theory B? and Solid applications of category theory in TCS?, many people shared their knowledge and opinions about the division of those two areas in theoretical CS.

I am a student in mathematics with experience in both graph theory and category theory, crucial mathematical knowledge for theory A and B, respectively, and I am seeking to learn more and probably even do some serious research in theoretical CS. I am interested in whether there are any intersections between theory A and B, and if so, are there any people who have done some work in the intersections or at least are there any references in this topic?
One cool example of work that straddles things that are typically considered theory A and things typically considered theory B are the lower bounds on the running time of the simplex algorithm with randomized pivoting rules, due to Friedmann, Hansen, and Zwick. The lower bounds rely on lower bounds for policy iteration algorithms for parity games, which are a tool used in formal verification and automata theory.