Re: Who invented n-categories?

["Ronald Brown" <ronnie@ll319dg.fsnet.co.uk>]

reply to r.brown@bangor.ac.uk

There is the following paper

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

which first defines  an n-fold category, specialises to an n-category,  and
relates that to a notion of globular set in (2.2), (2.3),  (without using
the term globular, which I think came from Pursuing Stacks, 1983).

Published at the same time was

33.  (with P.J. HIGGINS), ``The equivalence of $\omega$-groupoids
and cubical  $T$-complexes'', {\em Cah. Top. G\'eom. Diff.} 22
(1981) 349-370

which deals with the cubical, groupoid,  case (essential for the topological
applications) and of which some announcement was made in

22.  (with P.J. HIGGINS), ``Sur les complexes crois\'es,
$\omega$-groupo\"{\i}des et  T-complexes'', {\em C.R. Acad. Sci.
Paris S\'er. A.} 285 (1977) 997-999.

Were there earlier definitions? There was an unpublished manuscript by O.
Wyler (1972) referred to in 34, which my memory suggests did define n-fold
categories.

Ronnie Brown
http://www.bangor.ac.uk/~mas010

----- Original Message -----
From: <Topos8@aol.com>
To: <categories@mta.ca>
Sent: Monday, February 23, 2004 4:01 PM
Subject: categories: Who invented n-categories?


> Can anyone offer a reference to the first published work which defined a
> notion of strict n-category equivalent to that used today?
>
> I know that Ehresmann invented n-tuple ( or n-fold ) categories which
> contain strict n-categories as special cases.  If this is the first
> implicit defintion of strict n-category does anyone know who was the first
> to isolate our current notion of strict n-category as a particularly
> interesting special case of an n-tuple category?
>
> Carl Futia
>