Re: Two_questions

["Fred E.J. Linton" <fejlinton@usa.net>]

Salut, André,

I'm ashamed how long it took me to come to this realization, but
you were absolutely correct in your surmise that, when one lets ...

> ... E' be the set obtained from E by
> adding copy p' of p. There are two embeddings u,u':E-->E',
> the first u is the inclusion of E in E', and the second u' is defined 
> by putting u'(p)=p' and u'(x)=x for x different than p.

... the resulting u' is the same as the result of conjugating all the values
of u by the transposition t that exchanges p with p'. Thus, the ...

> ... pair of homomorphisms h,h':E!-->E'! the equaliser of which
> is the stabiliser S(p) of p in E!.

... that arises is exactly the same as the pair Sammy's argument 
would adduce, and the only respect in which ...

> This last argument seems to differ from the argument you have presented.

is that for Sammy it was enough to observe that h and h' differ SOMEWHERE  
when E is more than just {p}, while what you observe is rather more, namely, 
that h and h' actually differ EVERYWHERE other than on S(p), i.e., that the 
ONLY place where h and h' do NOT differ is S(p) :-) .

> Am I making an error?

Only in thinking that seeming difference makes any real difference :-) .

I hope this clarifies matters, and I think it's worth showing categories@mta.


Cheers,  -- Fred




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