Strictifying normal lax functors

Strictifying normal lax functors

[Jonathan CHICHE 齊正航]

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functors, and refers the reader to Bénabou's unpublished lectures as  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

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