In this paper, we prove that the polygraphic homology of a small category, defined in terms of polygraphic resolutions in the category ωCat of strict ω- categories, is naturally isomorphic to the homology of its nerve, thereby extending a result of Lafont and Métayer. Along the way, we investigate homotopy colimits with respect to the Folk model structure and deduce a theorem which formally resembles Quillen's Theorem A.

中文翻译：

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通过测谎仪的分类的同质性

在本文中，我们证明了一个小类别，在类别多图的分辨率来定义的印刷业同源ω猫严格的ω -类别，自然是同构于它的神经的同源性，从而延长乐峰和Métayer的结果。在此过程中，我们研究了与Folk模型结构有关的同伦同界，并推导了一个与Quillen定理A类似的定理。