For insight into John Baez's ideas around this time, try the slides from this colloquium: http://math.ucr.edu/home/baez/quantum_spacetime/
(http://math.ucr.edu/home/baez/quantum_spacetime/qs.pdf)
Urs Schreiber currently is at the forefront of where this line of mathematics ties in with fundamental physics. Here is a series he has started recently:
https://www.physicsforums.com/insights/20-years-ago-today-m-...
Baez's higher dimensional algebra program formed a large part of the heritage to these ideas.