Thanks Olivia, your answer goes right to the point, and really helps since it tells me why the arguing is legitimate. To all interested, see also the answers in mathoverflow. I see that to the experts the answer to my question was obvious. greetings e.d. On 24/07/13 08:04, Olivia Caramello wrote:

Dear Eduardo,

Your statement is valid internally in SS, that is once formalized in the internal language of the topos SS; this can be done in geometric logic, by considering a (possibly infinitary) disjunction over all the arrows f: C ---> X for C in CC (interpreted by the arrows Ff in SS) and existential quantifications. If you want a statement valid 'externally', you should instead use generalized elements in SS and epimorphic families involving their domains.

I hope this helps.

Best regards, Olivia

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