论文标题
André-Quillen的共同学和$ K $ - 纯粹的类别
André-Quillen Cohomology and $k$-invariants of simplicial categories
论文作者
论文摘要
使用Simplicial类别$ \ Mathcal {X} $的Dwyer-Kan-Smith共同体的Harpaz-Nuiten-Prasma解释，我们获得了André-Quillen共同学组的Cochain Complex，其中$ k $ invariants for $ k $ invariants for $ \ nathcal calcal calcal $ \ \ m nathcal {x} $ {x} $ {x} $ the tabt beality。给定简单类别的地图$ ϕ：\ Mathcal {y} \ rightarrow p^{（n-1）} \ Mathcal {x} $ to $ \ MATHCAL {x} $的nikov部分$ p^{（n）} \ mathcal {x} $。特别是，可以使用对立方体边界的这种障碍的明确描述来恢复$ \ Mathcal {x} $的各种高均匀副本不变性。
Using the Harpaz-Nuiten-Prasma interpretation of the Dwyer-Kan-Smith cohomology of a simplicial category $\mathcal{X}$, we obtain a cochain complex for the André-Quillen cohomology groups in which the $k$-invariants for $\mathcal{X}$ take value. Given a map of simplicial categories $ϕ:\mathcal{Y}\rightarrow P^{(n-1)} \mathcal{X}$ into a Postnikov section of $\mathcal{X}$, we use a homotopy colimit decomposition of $\mathcal{Y}$ to study the obstruction to lifting $ϕ$ to $P^{(n)}\mathcal{X}$. In particular, an explicit description of this obstruction for the boundary of a cube can be used to recover various higher homotopy invariants of $\mathcal{X}$.
