RE: categories with several compositions?

[N.Bowler@dpmms.cam.ac.uk]

I've just noticed there was a bit more to your question:

>More generally, a kind of category with several compositions:
>for each object y there is a set Dy and instead of the usual
>
>C(x,y) x C(y,z) -> C(x,z)
>
>we have   Dy -> [C(x,y) x C(y,z), C(x,z)]
>
>So you have a family of compositions at each object which "associate with
>each other" in the manner of the above equation, and where there is
>a single identity for each object.
I assume you would now want an identity at each object for each
composition. Then exactly the same argument as in my last email shows that
structures like this can be analysed in terms of categories C with a
designated family of (assignments to each object a of C of an invertible
endomorphism of a).

Nathan

PS There's a small typo in my last email. Replace `s_i' by `e_i'.


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