Re: Makkai's suggestion

[David Leduc <david.leduc6@googlemail.com>]

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:
>
> http://ncatlab.org/johnbaez/show/Towards+Higher+Categories

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.


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