A Survey of Definitions of n-Category

By Tom Leinster. Theory and Applications of Categories, 2001

162 citations recorded by the source corpus.

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 = 0, 1, or 2. The definitions can be read independently. Chatty bibliography follows.

Subfields: Computer Vision and Pattern Recognition, Geochemistry and Petrology, Information Systems

View Paper: https://www.semanticscholar.org/paper/4ac0d9ca6377246ff26150a0bfda6dd28c245388

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In Computer Vision and Pattern Recognition

In Geochemistry and Petrology

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Citations in the corpus

Higher Topos Theory (2006, background): “Several other possibilities are presented in the survey article [48].”
Polynomial functors and polynomial monads (2009, background): “For example, the set of natural numbers can be characterised as the least solution to the polynomial equation of sets X 1 + X ,”
Higher-dimensional categories: an illustrated guide book (2004, methodology): “In our discussions we took Leinster’s invaluable survey paper [69] as a starting point, and the present work might be treated as a companion to it.”
Derived Algebraic Geometry (2014, background): “Various other notions of∞-categories for which the compositions is only associative up to a coherent set of homotopies are gathered in [16, 84].”
Homotopy Theory of Higher Categories: THE MODEL STRUCTURE (2010, background): “Whereas the Batanin-type theories [20] [148] [162] are closest to this ideal, the Segal-type theories we consider in the present book will add additional structural sets to the basic globular set of A.”
Dendroidal Sets (2007, background): “Cat// is a dendroidal inner Kan complex capturing the notion of a bicategory with S as set of objects (see Bénabou [2]) or rather the notion of an unbiased bicategory (see Leinster [20]).”