论文标题
简单的方法，用于向颤音，标记类别，组和代数的路径同源性方法
Simplicial approach to path homology of quivers, marked categories, groups and algebras
论文作者
论文摘要
我们开发了Grigor'yan，Lin，Muranov和Yau（Glmy理论）在一般简单环境中引入的路径同源理论的概括。新理论包括特定案例的路径复合物和新同源性理论的特定情况：具有选定子集（标记组）的类别类别的路径同源性（标记类别）组和带有选择的载体矢量亚面的代数同源性的路径Hochschild同源性（标记代数）。使用我们的通用机械，我们还引入了一种新的同源性理论，该理论称为Quivers Quarterative Quivers的同源性，并将其与Grigor'yan，Muranov，Vershinin和Yau开发的理论进行了比较。
We develop a generalisation of the path homology theory introduced by Grigor'yan, Lin, Muranov and Yau (GLMY-theory) in a general simplicial setting. The new theory includes as particular cases the GLMY-theory for path complexes and new homology theories: path homology of categories with a chosen set of morphisms (marked categories) groups with a chosen subset (marked groups) and path Hochschild homology of algebras with chosen vector subspaces (marked algebras). Using our general machinery, we also introduce a new homology theory for quivers that we call square-commutative homology of quivers and compare it with the theory developed by Grigor'yan, Muranov, Vershinin and Yau.
