John Baez <baez@math.ucr.edu> wrote:
Yes: most or all of the successful approaches to infinity-categories follow a philosophy of this general sort. You can find a lot of references here:
Thank you for the reference. But I don't know where to start. Each author seems to be working with his own favorite special case of infinity-categories: (inf,1)-categories, opetopic and multitopic categories, simple omega-categories, theta-categories, protocategories... and so on. Is there a definitive definition of omega-categories somewhere in the literature or is it still unknown? Can it be stated in elementary terms (i mean in terms of object, arrows, ... without references to simplicial sets or topology) ? In the definition of a bicategory, one could replace the coherence axioms by the statement that all diagrams built from the canonical ismorphisms commute. Can it be generalized to n=3, ... , omega. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]