Geodesic
Segal's Multisimplicial Spaces
Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 11 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Some sufficient conditions on a simplicial space $X\!:\Delta^{op}\to\Top$ 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.
DOI : 10.2298/PIM141125001P
Classification : 18G30, 55P35, 55P48
Keywords: simplicial space, loop space, lax functor 
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     author = {Zoran Petri\'c},
     title = {Segal's {Multisimplicial} {Spaces}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {11 },
     year = {2015},
     volume = {_N_S_97},
     number = {111},
     doi = {10.2298/PIM141125001P},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM141125001P/}
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Zoran Petrić. Segal's Multisimplicial Spaces. Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 11 . doi: 10.2298/PIM141125001P

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