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Dec 11, 2012 at 18:07 comment added Todd Trimble Done. I also spelled out the universal argument at the end.
Dec 11, 2012 at 18:05 history edited Todd Trimble CC BY-SA 3.0
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Dec 11, 2012 at 17:30 comment added Almeo Maus Yes thank you, I think it would be more clear for me with the same notations as in the question (at least at the beginning). Thanks for the reference!! I will read it as soon as tomorrow.
Dec 11, 2012 at 17:17 comment added Todd Trimble If it helps, the universality argument at the end is a special case of Categories for the Working Mathematician (2nd ed.), p. 83, Theorem 2 (iv). It's good to go through the argument at least once in one's life.
Dec 11, 2012 at 17:11 comment added Todd Trimble No, sorry, that was an accident in transcription. I can change it if you want (and hope there were no other errors in transcription).
Dec 11, 2012 at 17:01 comment added Almeo Maus Thank you very much for your answer! However, I have to take some time to understand it. The $h$ in the question was $h : C' \rightarrow C$, but is it intentionally that you took $h : C \rightarrow C'$ ?
Dec 11, 2012 at 16:24 history answered Todd Trimble CC BY-SA 3.0