Omega-categories and chain complexes
Omega-categories and chain complexes
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欧米茄类别和连锁复合体
DOI：
10.4310/hha.2004.v6.n1.a12
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
R. Steiner
中科院分区：
文献类型：
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作者：
R. Steiner
有几种方法可以从组合对象中构建欧米茄范畴，例如粘贴方案或奇偶复合体。我们使这些结构成为一类具有附加结构的链复形上的函子，我们称之为增广定向复形。这个从增广有向复形到omega范畴的函子有一个左伴随，并且这个伴随限制于一个具有好基的增广有向复形范畴上的等价。与具有好基的增广有向复形等价的Ω范畴包括与球形、单形和立方体相关的Ω范畴;因此这些Ω范畴之间的态射由链复形之间的态射决定。因此，整个理论的欧米茄范畴可以表示在链复合物，特别是我们描述了双闭monoidal结构的欧米茄范畴和计算一些内部同态对象。
There are several ways to construct omega-categories from combinatorial objects such as pasting schemes or parity complexes. We make these constructions into a functor on a category of chain complexes with additional structure, which we call augmented directed complexes. This functor from augmented directed complexes to omega-categories has a left adjoint, and the adjunction restricts to an equivalence on a category of augmented directed complexes with good bases. The omega-categories equivalent to augmented directed complexes with good bases include the omega-categories associated to globes, simplexes and cubes; thus the morphisms between these omega-categories are determined by morphisms between chain complexes. It follows that the entire theory of omega-categories can be expressed in terms of chain complexes; in particular we describe the biclosed monoidal structure on omega-categories and calculate some internal homomorphism objects.