Re: double 2-categories

[Ondrej Rypacek <ondrej.rypacek@gmail.com>]

Thanks! I think a special case of a 4-fold category is precisely what
I'm after, I just didn't know what are they called beyond the double
case.

Ondrej




On 7 December 2010 14:13, Ronnie Brown <ronnie.profbrown@btinternet.com> wrote:
> 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
>

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