论文标题
造型的混音分辨率
Shuffle polygraphic resolutions for operads
论文作者
论文摘要
介绍了洗牌经营，以忘记对称作业的对称群体行动，同时保留所有可能的作品组合。然后，将重写方法应用于对称作业，通过洗牌经营：尤其是关于gröbner的概念，就树上的总订单而言，用于洗牌经营的概念。在本文中，我们介绍了混音测谎仪的结构，作为用于重写的分类模型，该模型通过消除单个秩序的限制以使重写规则的方向限制，从而概括了Gröbner基础方法。我们将w-operads定义为洗牌属性类别中的内部W分类。我们展示了如何将收敛的混合混合物延伸到由原始测谎仪的重叠分支产生的散档测量分辨率中。最后，我们证明了由二次收敛的混合散装测谎仪提出的洗牌作战是Koszul。
Shuffle operads were introduced to forget the symmetric group actions on symmetric operads while preserving all possible operadic compositions. Rewriting methods were then applied to symmetric operads via shuffle operads: in particular, a notion of Gröbner basis was introduced for shuffle operads with respect to a total order on tree monomials. In this article, we introduce the structure of shuffle polygraphs as a categorical model for rewriting in shuffle operads, which generalizes the Gröbner bases approach by removing the constraint of a monomial order for the orientation of the rewriting rules. We define w-operads as internal w-categories in the category of shuffle operads. We show how to extend a convergent shuffle polygraph into a shuffle polygraphic resolution generated by the overlapping branchings of the original polygraph. Finally, we prove that a shuffle operad presented by a quadratic convergent shuffle polygraph is Koszul.
