Re: Defining monoids

[JAMES STASHEFF <stasheff@email.unc.edu>]

For those who prefer to see the forests and the trees,
that point of view is prominent in the operad/modad/monoidal interaction.
Much such material will be in our book
on Operads (Markl and Shnider and me)

.oooO   Jim Stasheff		jds@math.unc.edu
(UNC)   Math-UNC		(919)-962-9607
 \ (    Chapel Hill NC		FAX:(919)-962-2568
  \*)   27599-3250

        http://www.math.unc.edu/Faculty/jds

On Thu, 6 Dec 2001, Charles Wells wrote:

> 
> 
> In talking about defining monoids, Toby Bartels wrote:
> 
> "We could also go straight to trees and define them as the basic operations,
> then requiring as axiom that grafting of trees produces the same result
> as composing the operations."
> 
> This is the mu operation of the corresponding monad.  Every single-sorted 
> "idea" in the sense of the recent discussion generates a monad in sets with 
> a mu like this.  For each set S there is a set of possible computations TS, 
> a mu:TTS to TS, and a "OneIdentity" operation in the sense of Mathematica 
> that says the computation consisting of a single node results in that node; 
> these subject to the monad laws.  In other words, the phenomenon you noted 
> is an instance of a general result.
> 
> --Charles Wells
> 
> Charles Wells,
> Emeritus Professor of Mathematics, Case Western Reserve University
> Affiliate Scholar, Oberlin College
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