A survey of (\infty, 1)-categories

Details A survey of (\infty, 1)-categories A survey of (\infty, 1)-categories

2006-10-09

arxiv.org/abs/math/0610239v1

Mathematics

Algebraic Topology

13 pages, written for the proceedings of the IMA workshop on n-categories

Scientific paper

In this paper we give a summary of the comparisons between different definitions of so-called (\infty,1)-categories, which are considered to be models for \infty-categories whose n-morphisms are all invertible for n>1. They are also, from the viewpoint of homotopy theory, models for the homotopy theory of homotopy theories. The four different structures, all of which are equivalent, are simplicial categories, Segal categories, complete Segal spaces, and quasi-categories.

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