Localization

Dear Colleagues, It is well known that one of possible model for the homotopy category there is the category Cat of small categories. Does anybody know a construction of a P-localization (P is a set of primes) using the categorical structure only? Many thanks in advance for your reply. With my best wishes, Marek G. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++