论文标题
离散同义理论的立方环境，重新审视
Cubical setting for discrete homotopy theory, revisited
论文作者
论文摘要
我们构建一个将立方体集与（简单）图相关联的函子。我们表明，以这种方式产生的立方组是KAN复合物，并且图的A组与相关KAN复合物的同型组一致。 我们用它来证明2006年Babson，Barcelo，de Longueville和Laubenbacher的猜想，以及在离散同型理论中的Hurewicz定理的强大版本。
We construct a functor associating a cubical set to a (simple) graph. We show that cubical sets arising in this way are Kan complexes, and that the A-groups of a graph coincide with the homotopy groups of the associated Kan complex. We use this to prove a conjecture of Babson, Barcelo, de Longueville, and Laubenbacher from 2006, and a strong version of the Hurewicz theorem in discrete homotopy theory.
