representable 2-functors

I would like to be able to place a good reference about representable functors from a weak 2-category (or a bicategory,--this is what Benabou considered) to Cat -the 2-category of all categories. For example the correspondence that takes each object to the corresponding representable 2-functor is a (weak) equivalence of 2-categories (analog of Yoneda's lemma). This, in particular, shows at once that any WEAK 2-category is weakly 2-equivalent to a STRICT one (where associativity for composition of 1-morphisms and the units arer strict). I suppose these things are well known to people, but what would be a good reference? Mikhail Kapranov ======================================