holomorph

Thank you to all people who contributed to the discussion about Cantor- Bernstein. I learnt many interesting things, although what I had I mind was rather the general categorical structure underlying the proof. A similar question could be asked about the "elementary" proof of the following theorem : if there is an injection from A to B, then there is injection from 2A to 2B. Another question. The construction of the holomorph of a group is well-known : Hol(G) = G x Aut(G) . Similar constructions can be done for graphs, categories, sketches, ... Has anyone seen anything about that ? Pierre Ageron