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 There was an unpublished manuscript by O. Wyler (1972) referred to in 34, which my memory suggests did define n-fold categories.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