Nonstrict notions of \(n\)-category and \(n\)-groupoid via multisimplical sets
type: Item
instance of: scholarly article
title: Nonstrict notions of \(n\)-category and \(n\)-groupoid via multisimplical sets
zbMATH Open document ID: 0934.18008
DOI: 10.1023/A:1007747915317
author: Zouhair Tamsamani
published in: \(K\)-Theory
publication date: 2000-04-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/alg-geom/9512006
review text: Following the idea that a category could be interpreted as a simplicial set, say, its nerve, the author gives a simplicial approach to the definition of a nonstrict \(n\)-category as an \(n\)-nerve. The author constructs a correspondence which to any topological space associates an \(n\)-groupoid \(\Pi_n(X)\) which generalises the Poincaré groupoid \(\Pi_1(X)\) and embodies the \(n\)-truncated homotopy type of \(X\). It is also shown in this paper that a suitable geometric realisation together with the given Poincaré groupoid, induces an equivalence between the category of \(n\)-groupoids and the category of \(n\)-truncated topological spaces. The paper also provides a proof of equivalence of the usual nonstrict bicategory with the simplicial construction for \(n=2\).
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 18B40
Mathematics Subject Classification ID: 18G30
Mathematics Subject Classification ID: 55U10
zbMATH DE Number: 1271718
zbMATH Keywords: simplicial set
zbMATH Keywords: \(n\)-category
zbMATH Keywords: \(n\)-nerve
zbMATH Keywords: Poincaré groupoid
reviewed by: Juan Antonio Pérez
MaRDI profile type: Publication
arXiv ID: alg-geom/9512006
OpenAlex ID: W2333114923
description: scientific article