与zeta级数有关的图的同伦代数
A homotopical algebra of graphs related to zeta series
摘要：
本文的目的是发展一个图的同伦代数，与有限图的zeta级数和谱有关。更确切地说，我们定义了一个奎伦模型结构的一类图（定向和可能无限的，允许循环和多个弧）。这个模型结构的弱等价是无环（保持循环的图态射）。该模型的上纤维化和纤维化是从Whiskerings（由嫁接树产生的图态射）类中确定的。我们的模型结构似乎很好地符合无环有向图在许多应用中的重要性。除了形成这个模型结构的弱因子分解系统，我们还描述了两个基于折叠，注入和覆盖图态射的Freelanc-Kelly因子分解系统。
英文摘要：
The purpose of this paper is to develop a homotopical algebra for graphs, relevant to zeta series and spectra of finite graphs. More precisely, we define a Quillen model structure in a category of graphs (directed and possibly infinite, with loops and multiple arcs allowed). The weak equivalences for this model structure are the Acyclics (graph morphisms which preserve cycles). The cofibrations and fibrations for the model are determined from the class of Whiskerings (graph morphisms produced by grafting trees). Our model structure seems to fit well with the importance of acyclic directed graphs in many applications. In addition to the weak factorization systems which form this model structure, we also describe two Freyd-Kelly factorization systems based on Folding, Injecting, and Covering graph morphisms.
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