# A survey of definitions of n-category

## Tom Leinster

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.

Keywords: n-category, higher-dimensional category, higher categorical structure.

2000 MSC: 18D05, 18D50, 18F99, 18A99.

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.ps

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