Dear Jean, I remember you talking about foliations more than 20 years ago, but when exactly is this done? Long before? No matter what was done first, I think it would nice to compare this carefully with the results of [C. Cassidy, M. H?bert, and G. M. Kelly, Reflective subcategories, localizations, and factorization systems, Journal of Australian Mathematical Society (Series A), 1985, 287-329]. The seemingly big difference is that the above-mentioned paper is about reflections, but in fact having the right adjoint is a much weaker restriction than it seems (in this context). Since we don't sent attachments to Categories mailing list, I shall send you that paper separately. With best regards to all, George [For admin and other information see: http://www.mta.ca/~cat-dist/ ]