小范畴上同调的方向函子方法
A direction functor approach to the cohomology of small categories
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中文总结 AI 辅助
该研究提出用方向函子构建Barr-正合范畴和S-Maltsev范畴的上同调理论，并证明其与Hoff等引入的小范畴上同调理论等价。
中文摘要 AI 辅助
我们展示方向函子可用于为Barr-正合范畴和S-Maltsev范畴构建上同调理论，其中S是带有固定截面的一类特定满态射。利用对任意集合B，以B为对象集的小范畴范畴关于Schreier点类是S-Maltsev范畴这一事实，我们证明由方向函子导出的小范畴上同调理论与Hoff和Golasinski引入的理论一致。
英文摘要
We show how the direction functors can be used to develop a cohomology theory for Barr-exact and S-Maltsev categories, where S is a suitable class of split epimorphisms with a fixed section. Using the fact that, for any set B, the category of small categories with B as set of object is S-Maltsev with respect to the class of Schreier points, we show that the cohomology theory of small categories arising from the direction functors coincides with the one introduced by Hoff and Golasinski.
