We show that the canonical homotopy theory of strict 2-categories embeds in that of $(\infty ,2)$-categories in the form of 2-(pre)complicial sets. More precisely, we construct a nerve-categorification adjunction that is a Quillen pair between the canonical model structure for 2-categories and the model structure for 2-precomplicial sets. Furthermore, we show that the former model structure is transferred along this nerve and that the nerve is homotopically fully faithful.

中文翻译：

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2-categories 的神经和 (∞,2)-categories 的 2-categorification

我们证明了严格 2-范畴的规范同伦理论嵌入 $(\infty ,2)$-以 2-（预）复杂集形式存在的类别。更准确地说，我们构建了一个神经分类附属，它是 2 类别的规范模型结构和 2 预并发症集的模型结构之间的 Quillen 对。此外，我们表明前一个模型结构沿着这条神经转移，并且该神经是同位完全忠实的。