[FOM] Fraenkel-Mostowski-Specker method and category theory
V. Yu. Shavrukov
vshavruk at science.uva.nl
Mon Apr 3 17:07:59 EDT 2006
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
> 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
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