internal hom of the omega-category of omega-categories: my own attempt

Dear all, I read somewhere that strict omega-categories are well understood (unfortunately, not by me). I hope someone knowledgeable can help me with the problem below. Let C and D be strict omega-categories. One can build the following strict omega-category that I call [C,D] : objects = functor from C to D hom_[C,D] (F, G) = Product_{X in C} hom_D (F X, G X) This construction can be extended to an omega-functor [_,_]. Is [_,_] the internal hom of the omega-category of omega-categories? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]