Many people have proposed definitions of `weak n-category'. Ten of them are presented here. Each definition is given in two pages, with a further two pages on what happens when $n\leq 2$. The definitions can be read independently. Chatty bibliography follows.
Theory and Applications of Categories, Vol. 10, 2002, No. 1, pp 1-70 http://www.tac.mta.ca/tac/volumes/10/1/10-01.dvi http://www.tac.mta.ca/tac/volumes/10/1/10-01.ps http://www.tac.mta.ca/tac/volumes/10/1/10-01.pdf ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/1/10-01.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/1/10-01.psTAC Home