Dear all, Given a 2-category C, there is a 2-category C' and a normal lax functor from C to C' such that, for any normal lax functor from C to a 2-category D, there is a unique strict 2-functor from C' to D which makes the triangle commute. (To avoid any confusion: I take normal lax functor to be what is defined in, say, p. 7 of the paper http:// arxiv.org/abs/0909.4229.) Gray, in "Formal Category Theory", I,4.23, Appendix A (p. 92), gives an analogous universal construction with respect to general oplax functors, and refers the reader to Bénabou's unpublished lectures as a more general reference. I have seen a reference to Theorem 3.13 of the Blackwell-Kelly-Power paper "Two-dimensional monad theory" (JPAA 59 (1989, 1-41), thanks to Matias del Hoyo for pointing that to me), but I do not have it handy and I am unsure whether the general theorem provides a much concrete description of the universal 2- category in the particular case I am interested in (and I do not know whether the normalized case falls into its range of application). Are there references dealing specifically with normalized (op)lax functors? Is there an explicit description of this universal construction I could refer to in the literature? Thanks in advance! Best wishes, Jonathan [For admin and other information see: http://www.mta.ca/~cat-dist/ ]