Dear Gerard:

Just a few minor editorial comments on the improved version.
	
      0. Abstract          
Line 5, functions misspelt.

--> done

1.Introduction
Acknowledgements misspelt (I thought this was automatic in LaTeX, maybe that was why I missed it before.   (I note that Stasheff also found the reference to Catherine Borgen opaque; also, is it accurate, as the input from Stasheff must have occurred after the last part was prepared.)

--> done

Line 4 of  Acknowledgements should be advantage.
(We assume  Introduction is on Page 1 for correction purposes.)

--> done

2.References It gives an unfortunate impression to have the references start with [3] and then go on to [15].

--> [1] was present but not [2]. Suppressed unused references. 

>>This should be done even for an arXiv deposit as otherwise it makes the file seem hastily prepared. 

-->100% agreed

correct reference [15] is       J. Phys.: Conf. Ser. 30 107-118 (2006)

--> corrected, I maintained also the ArXiv references (for my friends mathematicians)

I am not sure what the status of References [39] and [40] is; perhaps these should be arXiv'ed and the arXiv references given?

--> I do not know, skipped then

3.Eq(1)  is there a special significance to := ? (Elsewhere “=”  is used.)

Yes, it is to mark definition 

4.After Eq(2)  normalize not renormalize (which has a special meaning to physicists.)

--> done

5.Bottom of Page 2, footnote §. Reference to Bourbaki is unnecessary here.


--> Not for me ... and it is not wrong anyway.

6.Page 3, line -4:  consecutive “i”s look funny in English; use “multi-index”.
(Also elsewhere – use automatic replace to find other examples.)

--> done everywhere

7.Eq(12) should finish with a “.” then new sentence “The alphabet...”

--> done

8.Page 14/15 Prop 5.1: The * is used both fro A* and for left append  which is confusing. Suggest that you use A#  for the set of lists as otherwise A* suggests a type of conjugation. 

--> If you look closer, you will see that the two stars ("*") were not given at random. They are the mark of the "free monoid" and "*" is for free products in category theory. These denotations are classic in Computer Science, Combinatorics and in Discrete Math. Moreover there is no semantic confusion as one star is in infix position and the other (throughout the paper for example as well with $(\mathfrak{MON}^+(X))^*$) is in exponent position. 

9.Page 16, Lemma 5.2:    First line of Lemma  (whose law will....)

--> done

 Third line of Lemma  We will denote by T^n..


--> done

10. Page 20 , last line before References: not developped but developed.

--> done

Thanks,  Gérard