As Don McInnes observed in his letter of 1 July to Categories, there are indeed fine distinctions to be made between (a) categories with limits of some class and functors that preserve these, in the usual "to within isomorphism" sense, and (b) categories with chosen limits of some class and functors which preserve these on the nose. Only the latter is a direct example of "universal algebra", leading to monadicity and so on; but the former is also of great importance. One of the theorems in [Blackwell, Kelly, and Power, Two-dimensional monad theory, JPAA 59 (1989),1 - 41] shows that the free objects for the (b) context are also "free objects" for the (a) context, but now of course with an equivalence where there had been an isomorphism. It is, however, only more recently that some of us sorted this out more completely - and learned that we ourselves had sometimes uttered inaccuracies in the past. There is a careful discussion of some such points in the Introduction of [Ada'mek and Kelly, M-completeness is seldom monadic over graphs, TAC 7 (2000), 171- 205]. That same paper, in its final section "5. Appendix on saturation", contains the important Theorem 5.5, which was later used in Section 4 of [Kelly and Lack, On the monadicity of categories with chosen limits, TAC 7 (2000), 148 - 170], to show what kind of relation subsists between the 2-monad, for instance, for "all finite limits" and the 2-monad for "binary products, a terminal, and equalizers"; they are in fact equivalent but not isomorphic. I apologize for the sparcity of detail above; I don't have all these papers before me as I write, nor the time to down-load them just now. Regards to all - Max Kelly.