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I have an objection to this. If you see the discussion over at evil, there really isn't a very good way to define "composability" non-evilly without resorting to some black magic like type theory.
Your LaTeX is broken also =(.
I think you may want to reformat it as well, because it's very hard to read at the moment. It's basically a giant block of text. In particular, it might be worth it to split your diagrams out as displays. Also, please write composition in the normal way. It's really hard to follow articles that are typed up using two different notations. If you feel that strongly about it, you might be able to convince the steering committee, but I kinda doubt it.
I've also gone ahead and rewritten the "for every composable string of morphisms in " into "for every composition in ", and the same for the n-ary case, with this hopefully now being acceptable wording for "for all objects in , for all morphisms in ", etc. That's all I ever meant by the original wording, anyway.
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