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From: "Prof. Peter Johnstone"
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Subject: Re: categories with several compositions?
Date: Wed, 2 Feb 2011 15:17:42 +0000 (GMT)
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On Wed, 2 Feb 2011, John Stell wrote:
>
> Can anyone tell me whether these structures have been studied anywhere?
>
> A kind of generalized monoid with two or more compositions *1, *2, etc
> with a single identity that works for both and where
> (x *i y) *j z = x *i (y *j z) for all i,j
>
Substituting the common identity for y in this equation yields
x *j z = x *i z, so the compositions all coincide. Similarly
in the multiple-object case.
Peter Johnstone
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