论文标题
Gabriel-Zisman的辅助和光谱序列
Gabriel-Zisman Cohomology and spectral sequences
论文作者
论文摘要
扩展了Gabriel和Zisman的构造，我们为简单组合的同源和同源性开发了功能框架，该组合具有由函数在Abelian类别中给出的非常通用的系数系统。此外，我们为任何简单集的图构建Leray类型频谱序列。我们还表明，这些构造概括并统一了小类的共同体和同源性的各种现有版本，并且作为奖励提供了对其功能性的新见解。
Extending constructions by Gabriel and Zisman, we develop a functorial framework for the cohomology and homology of simplicial sets with very general coefficient systems given by functors on simplex categories into abelian categories. Furthermore we construct Leray type spectral sequences for any map of simplicial sets. We also show that these constructions generalise and unify the various existing versions of cohomology and homology of small categories and as a bonus provide new insight into their functoriality.
