Dear Jim,

Actually some corrections had already occured.
Below, the state of affairs. 
May I include you in the aknowledgements ?

With my best regards
Gérard
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>>There was no ^d in the list of affiliations
>>The Open U had  ^e

done. Thank you, this escaped.

>>generic after displays: \noindent

corrected.

>> abstract: in A simplified

already done.

>>p.1  co-addition instead of the usual comultiplication?

yes, I added a footnote because I would like that the reader 
saw this as a part of the theory of "representative functions" 
rather than the traditional coproduct. 

>>reminiscent OF Hoffmann's

had been done

>>three-parameter (no s)

had escaped, thank you.

>>the stay of the firs 

a private house

>>Be it's owner -->  May ... is she really the OWNER? was it a lodging?

changed. 

>> p.8 as shows --> as is shown

changed by "as shown" 

>> p. 13 We do the extra?? We add the extra?

changed by "We make an extra hypothesis"

>>p.15 enveloping (one p) and the relation of primitive to enveloping 
>>should have been recalled at the time you first mention primitive
 
had been done

>>first bullet: do not understand what your are trying to say

as apprears in Fig5, the letters (generators in the free case) of the monoid are the diagrams that possess only "one" black spot.

>>where are crossings and superpositions defined - perhaps
I skimmed too fast -  diagram 6 only confuses me

I have put a footnote in order to make this point clearer.

>>p.18 is shifting just a technical computational device or does it mean something?

yes, it does. This phenomenon occurs ubiquitously in algebraic combinatorics where it is often due to a translation of the indices in the alphabet of variables (shifted concatenation, shifted shuffle etc...) 

>>p.19 why is it called phase space

meant space of all possible valid configurations. Can replace it by "variety".

>>p.21 structure of listS

had escaped, thanks.

>>p.22 final paragraph: 

>>how are they structurally different?
>>can't any parameter correspond to perturbations?
>>do you distinguish deformations from parameters?

you're right. I replaced it by "are of different nature". I want to express here that $q_c$ is a deformation of the tensor structure whereas $q_s$ is a perturbation of the law dual to the product.