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Feb 22, 2011 at 16:16 comment added Finn Lawler Yes, I meant possibly-infinite terms. The initial/terminal (co)algebras are those of distinct functors (see edits to question). I don't know about your example, but it reminds me of Barr's paper about terminal coalgebras as Cauchy completions of initial algebras.
Feb 22, 2011 at 14:00 history answered Andrej Bauer CC BY-SA 2.5