RE: categories with several compositions?

[John Stell <J.G.Stell@leeds.ac.uk>]

Thanks for pointing that out.
I should have been asking for each composition to have its own identity

John 

-----Original Message-----
From: Prof. Peter Johnstone [mailto:P.T.Johnstone@dpmms.cam.ac.uk] 
Sent: 02 February 2011 15:18
To: John Stell
Cc: 'categories@mta.ca'
Subject: Re: categories: categories with several compositions?

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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