In this paper we complete a chain of explicit Quillen equivalences between the model category for ${\mathrm{\Theta }}_{n+1}$‐spaces and the model category of small categories enriched in ${\mathrm{\Theta }}_n$‐spaces. The Quillen equivalences given here connect Segal category objects in ${\mathrm{\Theta }}_n$‐spaces, complete Segal objects in ${\mathrm{\Theta }}_n$‐spaces, and ${\mathrm{\Theta }}_{n+1}$‐spaces.

中文翻译：

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（∞，n）分类模型的比较II

在本文中，我们完成了以下模型类别之间的显式Quillen等价链： ${\mathrm{\Theta }}_{ñ+\mathrm{1个}}$-空间和小类别的模型类别丰富了 ${\mathrm{\Theta }}_{ñ}$空格。此处给出的Quillen等价关系将${\mathrm{\Theta }}_{ñ}$空格，完整的Segal对象 ${\mathrm{\Theta }}_{ñ}$空格 ${\mathrm{\Theta }}_{ñ+\mathrm{1个}}$空格。