On 26/09/2010, at 12:00 PM, David Leduc wrote:
All the constructions I can find rely on strict omega-categories defined as graphs with structure. If instead we define recursively a strict omega-category as a category enriched over a strict omega-category, is there a recursive way to define the omega-category of omega-functors (between two fixed omega-categories)?
Dear David Let V be a finitely complete cartesian closed category. Then both the category Cat(V) of categories in V and the category V-Cat of small categories enriched in V are also cartesian closed. If V = Set then Cat(V) = V-Cat = Cat. If V = Cat then Cat(V) = Dbl is the category of double categories and double functors while V-Cat = 2Cat is the category of 2-categories and 2-functors. If V = 2Cat then V-Cat = 3Cat . . . and on it goes. Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]