Re: double 2-categories

[Ronnie Brown <ronnie.profbrown@btinternet.com>]

I am not sure why there is the restriction to having 2-categories as
edge arrows. They could be double categories, perhaps.  Would this then
be any more general than a 4-fold category?

A definition of n-fold category is given in

34.  (with P.J. HIGGINS), ``The equivalence of $\infty$-groupoids and
crossed  complexes'', {\em Cah. Top. G\'eom. Diff.} 22 (1981)
371-386.

and this also contains a definition of what was later called a globular
set, giving a notion of what we now call a strict globular n-category,
though the emphasis in the paper is on the groupoid case.

Ronnie

On 07/12/2010 12:59, Ondrej Rypacek wrote:
> Dear all,
>
> Is there a standard reference for what could be called a double-2-category,
> by which I mean a double category where the categories of horizontal and
> vertical arrows are 2-categories ?
> It would be a special case of a "triple category", I guess, where
> there are objects, arrows in three directions, cells for each distinct
> pair of the directions, and cubes surrounded by cells.
>
>
> Many thanks,
> Ondrej
>

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