Homology, Homotopy and Applications

Volume 18 (2016)

Number 2

Brown categories and bicategories

Pages: 217 – 232

DOI: https://dx.doi.org/10.4310/HHA.2016.v18.n2.a12


Geoffroy Horel (Max Planck Institute for Mathematics, Bonn, Germany)


In a Brown category of cofibrant objects, there is a model for the mapping spaces of the hammock localization in terms of zig-zags of length $2$. In this paper we show how to assemble these spaces into a Segal category that models the infinity-categorical localization of the Brown category.


relative category, infinity-category, localization, Brown category, Tamsamani category

2010 Mathematics Subject Classification

18D05, 18G30, 18G55

Published 29 November 2016