Geodesic
Segal's Multisimplicial Spaces
Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 11

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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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     title = {Segal's {Multisimplicial} {Spaces}},
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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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