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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]