A couple of months ago, there was a discussion in this forum about categorical formulations of the Axiom-Scheme of Replacement. From this, no fewer than four approaches emerged, as follows: (1) Steve Awodey considered Algebraic Set Theory (2) Colin McLarty considered an Elementary Theory of the Category of Sets (3) Thomas Streicher considered Universes (4) I (Paul Taylor) considered iterations of a functor indexed by a well founded coalgebra. (I was going to write a one-paragraph summary of each of these, but decided that the risk of error was too great.) Following the public discussion, the four of us, together with Mike Shulman, who had raised the question in the first place, continued it in private for a while. What I wanted to achieve from this was some agreement on a metalanguage for the classes (such as a Heyting pretopos) and a statement of each formulation within this metalanguage. Then someone (else) could compare the definitions, and ask to what extent they are equivalent. (I don't want to re-open the substantive discussion at the moment, but I should point out that the objective of my formulation was to avoid the need for such a metalanguage, although this is needed to compare my view with the others.) We didn't manage to do this, but the five of us adjourned our discussion, with an agreement to re-open it later. One possibility is the Category Theory meeting in Calais next month, and I suggested to the Programme Committee that they might set aside a room for a parallel session devoted to this topic. In their response, they seem to have interpreted the proposal in a rather more formal way than we had intended. Also, it turns out that, of the five, only Steve and I will be present. So, to get to the point, Steve and I invite anyone who would like to take part in a discussion (of whatever degree of formality) about Replacement during the course of the conference to contact us privately, so that we can make arrangements with the programme committee. Paul Taylor pt08@PaulTaylor.EU Steve Awodey awodey@cmu.edu