TL;DR
This paper constructs a Segal category model for the infinity-categorical localization of Brown categories of cofibrant objects, using zig-zags of length 2 to represent mapping spaces in hammock localizations.
Contribution
It introduces a method to assemble mapping spaces into a Segal category that models the infinity-categorical localization of Brown categories.
Findings
Mapping spaces can be modeled by zig-zags of length 2.
Segal categories effectively represent the infinity-categorical localization.
Provides a new construction for localizations in homotopical categories.
Abstract
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.
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