Dear Experts in Category Theory, I am very interested in the following problem. Let us consider the category Cat of small categories. I need for a "topology" on Morph(Cat) (i.e., the functors between small categories), with the following property: For each u in Morph(Cat) and each D in Ob(Cat) there exist v C------------>D in Morph(Cat), a functor F:Cat----->Cat with F(u) = v, and two "open neighbourhoods" U and V of u and v, respectively, such that F (acting on Morph(Cat)) is a "homeomorphism" between U and V. I would be very grateful to you for any related comment. With my best regards, I remain Truly Yours Adrian Duma. ____________________________________________________________________ Get free email and a permanent address at http://www.netaddress.com/?N=1