Equivalence de la th\'eorie homotopique des $n$-groupo\"{i}des et celle des espaces topologiques $n$-tronqu\'es

Abstract

This paper constitutes a recent work using the constructions of a previous preprint alg-geom/9512006 to show that the functors geometric realisation and Poincar\'e $n$-groupoid induce an equivalence between the category of $n$-grouppoids and the category of $n$-truncated topological spaces, when we localise both categories by weak equivalence.