horizontal composition in a 2-category

Hi, A 2-category C is a category enriched over Cat. This gives me two compositions. * The functor C(Y,Z) x C(X,Y) -> C(X,Z) * and for each X and Y in C the function (C(X,Y))(g,h) x (C(X,Y))(f,g) -> (C(X,Y))(f,h) But how can I derive the horizontal composition: (C(Y,Z))(g1,g2) x (C(X,Y))(f1,f2) -> (C(X,Z))(g1 o f1, g2 o f2) = ??? I the case of the 2-category of categories, I know how to define horizontal composition (Godement product) in a pointwise manner, but how does it generalize to 2-categories? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]