Comma 2-categories (reference request)

Comma 2-categories (reference request)

[Jonathan CHICHE]

Dear all, 

It has recently been pointed out to me by a referee that two constructions of which I make use (among which a 2-dimensional Grothendieck construction) were special cases of comma 2-categories. The references given in the rapport are sections 1.2.5 of Gray's "Formal category theory" and section 4 of Kelly's "On clubs and doctrines". The first one deals with strict 2-functors whereas the second one limits itself to lax functors whose domains are categories. 

Are there other references dealing with more general cases? In any case, what are other references spelling out functoriality properties? (There are some in these two texts and I could work out what I need, but the more references the better.) 

Thanks. (And thanks to the referee, whom I am not supposed to contact directly.)

Jonathan

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