Segal's multisimplicial spaces

Abstract

Some sufficient conditions on a simplicial space $X$ guaranteeing that $X_1\simeq \Omega |X|$ were given by Segal. We give a generalization of this result for multisimplicial spaces. This generalization is appropriate for the reduced bar construction, providing an $n$-fold delooping of the classifying space of a category.

12 pages