2015/05/19 by Zoran Petric, Petric, Zoran
Mathematics · #18G30 #55P35 #57T30 #Category Theory (math.CT) #FOS: Mathematics #math.CT #msc:18G30 #msc:55P35 #msc:57T30
paper · pdf · doi:10.48550/arxiv.1505.05010
10 pages
arxiv created 2015/05/19 · arxiv updated 2015/05/20
A characterization of simplicial objects in categories with finite products obtained by the reduced bar construction is given. The condition that characterizes such simplicial objects is a strictification of Segal's condition guaranteeing that the loop space of the geometric realization of a simplicial space X and the space X1 are of the same homotopy type. A generalization of Segal's result appropriate for bisimplicial spaces is given. This generalization gives conditions guaranteing that the double loop space of the geometric realization of a bisimplicial space X and the space X11 are of the same homotopy type.