论文标题
双$（\ infty，1）$ - 双类别的分类神经
A double $(\infty,1)$-categorical nerve for double categories
论文作者
论文摘要
We construct a nerve from double categories into double $(\infty,1)$-categories and show that it gives a right Quillen and homotopically fully faithful functor between the model structure for weakly horizontally invariant double categories and the model structure on bisimplicial spaces for double $(\infty,1)$-categories seen as double Segal objects in spaces complete in the horizontal direction.然后，我们沿着两类的同质水平嵌入沿同型水平嵌入到双类别中，并证明它在拉克的2类模型结构与2倍完整的Segal空间的模型结构之间提供了正确的Quillen和同型完全忠诚的功能。我们进一步表明，缺乏的模型结构是从模型结构中直接引起的，该模型结构是2倍完整的Segal空间。
We construct a nerve from double categories into double $(\infty,1)$-categories and show that it gives a right Quillen and homotopically fully faithful functor between the model structure for weakly horizontally invariant double categories and the model structure on bisimplicial spaces for double $(\infty,1)$-categories seen as double Segal objects in spaces complete in the horizontal direction. We then restrict the nerve along a homotopical horizontal embedding of 2-categories into double categories, and show that it gives a right Quillen and homotopically fully faithful functor between Lack's model structure for 2-categories and the model structure for 2-fold complete Segal spaces. We further show that Lack's model structure is right-induced along this nerve from the model structure for 2-fold complete Segal spaces.
