August 22, 2022
As anyone who knows me may know, I have been working on reading Alain Badiou's Mathematics of the Transcendental for a few years now. And as you may not know, I am currently studying the evolution of networks and graph theory, specifically the Greatest Strongly Connected Component.
I am still baffled and relatively starved of a good resource to contextualize category theory, though I sense its power in the Badiou. I attempted to read a paper about applications of category theory, but there was still some context lacking. I am still very much a very OCD individual, and need the context for why things arise as much as I need the how of how they arise.
One of the common themes I see here is that references in category theory that denote an option most referred to by other categories would be an equivalent to the GSCC. The difference being the interrelations between the other terms have not yet been mapped, nor necessarily have to be in the strictly categorical system. Only when they become a living system, inter-referring, do they begin to be embedded on a graph.
I see potential for analysis of analytical systems themselves using what I am currently learning about the "spring' function in graph theory. I will have to see how category theory and graph theory interrelate first. Off to do that!
