[FOM] Fraenkel-Mostowski-Specker method and category theory

[solovay@Math.Berkeley.EDU]

>
> On Apr 3, 2006, at 18:18, solovay at math.berkeley.edu wrote:
>>      My question is this: Are (a) and (b) the only reasons that two
>> such
>> categories are equivalent. That is, if C(G_1, Gamma_1) and C(G_2,
>> Gamma_2) are equivalent then are there subgroups H_1 of G_1 and H_2
>> of G_2 [lying in the respective filters] such that letting Gamma_1'
>> and Gamma_2' be the evident restricted filters we have C(H_1,
>> Gamma_1') equivalent to C(H_2, Gamma_2').
>
> I must be missing something about this question.  Isn't the answer
> automatically yes once we put  H_1 = G_1  and  H_2 = G_2 ?  I feel
> tempted to replace the conclusion by  (H_1, Gamma_1')  isomorphic to
> (H_2, Gamma_2').
>
>
> regards,
> Volodya Shavrukov

You are right. I stated my question wrongly and what I intended is your
proposed repair.

     --Bob
>
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