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arXiv · 1012.1541

In the category of relative categories the Rezk equivalences are exactly the DK-equivalences

C. Barwick·D. M. Kan
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Abstract

In a previous paper we lifted Charles Rezk's complete Segal model structure on the category of simplicial spaces to a Quillen equivalent one on the category of "relative categories," and our aim in this successor paper is to obtain a more explicit description of the weak equivalences in this model structure by showing that these weak equivalences are exactly the DK-equivalences, i.e. those maps between relative categories which induce a weak equivalence between their simplicial localizations.

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C. Barwick, D. M. Kan. 2010-12-07. In the category of relative categories the Rezk equivalences are exactly the DK-equivalences. https://arxiv.org/abs/1012.1541

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