What category would it go under? Under "Setting" we have "Technology", "People", "Places", "History", and "Language". Fighting styles don't seem to fit into any of those categories. Maybe it should be its own?
Styles can also go under sub-categories:
Martial arts -- The various Asian arts, Battle Angel Alita's "Panzer Kunst" cyborg fighting style, and the Sora Mai are prime examples. These have highly defined moves (kata, forms, whatever they may be called) that the user can string together to devastating effect. Normal mastery takes decades of practice, but the SARP setting allows possibility for some shortcuts to be taken for cyborgs and artificial life forms.
Brawling -- The more free-form styles. These teach you how to fight fights in ways that demand that you outlast your opponent, but also focusing on max damage and placing it where it'll most quickly take out your target. CQC (Close-Quarters Combat), Krav Maga, Muay Thai (Thai kickboxing), and American boxing would go here, as would most hybrid styles of martial arts. PRO/D is an SARP example of a brawler fighting style, albeit a rather strange one.
Self-defense -- the sort useful for delaying an attacker while help arrives or to allow the attacked to get away, possibly referred to as "Martial Arts Lite". Basically take the lethal aspects of the martial arts away and give the person only enough to survive. They will be far from highly-trained professionals, but it will give them an edge to give users a better chance against brawlers. Also popular as exercise routines. Tai Bo and Tai Chi are good examples (though Tai Chi is possibly practical for actual fighting, given enough practice).
Armed Fighting -- these styles are tempting to mix in with the others, but if a certain style relies on weapons completely (such as the Gun Kata techniques from the film "Equilibrium"), then that should be in this sub-category. Jutsu, Wushu, and Sora Mai cover weapons training in addition to the hand-to-hand portion of their styles, so they would remain in the main Martial arts sub-category and NOT be in this one.
PA Combat, starship tactics, and urban warfare primers also might be a good idea to include. Perhaps under a "Misc. Combat Techniques & Tactics" sub-category?
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Does all of this sound reasonable? So it would go "Setting">"Fighting Styles"> (the sub-categories mentioned) and players would create pages under those sub-categories for their styles.
The main problem I would see with this create-your-own-style thing is descriptions and approval. Some styles can be very, very powerful, but we would need to keep in mind that one in millions or billions would be true masters of their style and less than that would become masters of multiple styles (excepting possible cybernetic/artificial enhancements). So anyone fighting would never be able to use a style 100% effectively, since these fights are usually quick and mistakes can be made on the fly. So a style portrayed as "perfect" will never (should never) be played as such. It may be perfect in theory, while in practice it will never be.
Also, for characters using a Martial Arts style (not Brawling), they would be required to keep their practice up (mention it every few days ICly or something, nothing too difficult) or suffer loss of effectiveness over time. Brawlers would need a similar requirement, except theirs would be in strength and reflex training and conditioning, not kata practice. I suppose it would be the difference between playing a rogue and a warrior: One relies on speed and agility, the other on strength and stamina.
Sorry for the long post...I just got rolling when I started typing, but I hope this all turns out useful. If half of what I wrote is usable, then I count it a success : D