On non-strict notions of $n$-category and $n$-groupoid via multisimplicial sets
Abstract
In this paper we first give a simplicial approach to the definition of a non strict -category that we call an -nerve following the idea that a category could be interpreted as a simplicial set, and we prove that our construction generalises the case of the usual non strict 2-category. Next we give a simplicial definition of a non strict -groupoid. Then we associate to any space an -groupoid which generalises the famous Poincar\'e groupoid and embodies the -truncated homotopy type of . We also give a natural construction for the geometric realisation of an -groupoid and we conjecture that the functor geometric realisation is an inverse up to equivalence to the functor from the category of -truncated topological spaces to the category -Gr of -groupoids.
Cite
@article{arxiv.alg-geom/9512006,
title = {On non-strict notions of $n$-category and $n$-groupoid via multisimplicial sets},
author = {Zouhair Tamsamani},
journal= {arXiv preprint arXiv:alg-geom/9512006},
year = {2015}
}
Comments
Plain TeX, In French. e-mail: [email protected] (with ``for Tamsamani'' in subject)