Geodesic
A survey of definitions of n-category
Theory and applications of categories, Tome 10 (2002), pp. 1-70.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.
Classification : 18D05, 18D50, 18F99, 18A99.
Keywords: n-category, higher-dimensional category, higher categorical structure. 
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Tom Leinster. A survey of definitions of n-category. Theory and applications of categories, Tome 10 (2002), pp. 1-70. http://geodesic.mathdoc.fr/item/TAC_2002_10_a0/