question concerning lax functors

question concerning lax functors

[Matias del Hoyo]

Hi, I'm Matias del Hoyo from Buenos Aires and I wonder if someone
could help me by giving some reference about the following.

If 2Cat is the category of (strict) 2-categories and (strict)
2-functors, and Lax is the category of (strict) 2-categories and
(normal) lax functors, then I guess that the inclusion 2cat --> Lax
admits a left adjoint, namely for a 2-category C there is another FC
and a lax functor i:C --> FC such that for every lax functor v:C --> D
there exists a unique 2-functor u:FC --> D satisfying v=ui.

In my thesis I constructed FC in the case C is a category (2-category
with trivial 2-cells) by using subdivision of small categories. This
was enough for my purpose (a version of Quillen's Thm A for lax
functors), but the general case might be of interest and it should be
well known.

Thanks in advance!
Matias del Hoyo


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