论文标题
鱼堆：阵列，广义关联和堆
Heaps of Fish: arrays, generalized associativity and heapoids
论文作者
论文摘要
在本文中，我们通过定义扩展张量网络，类别和关系代数的通常概念的超图的图表来研究关联的三元概括。这样一来，我们重新发现了称为堆的三元结构，并能够在匕首类别及其概括的背景下对其融合进行更全面的处理。我们的主要见解是将关联作为HyperGraph重写系统的汇合属性。这种方法使我们能够定义一个三元类别和巨人的概念，其中形态同时结合了三个对象，并提出了对较高敏捷性缔合性形式的系统研究。
In this paper we investigate a ternary generalization of associativity by defining a diagrammatic calculus of hypergraphs that extends the usual notions of tensor networks, categories and relational algebras. In doing so we rediscover the ternary structures known as heaps and are able to give a more comprehensive treatment of their mergence in the context of dagger categories and their generalizations. Our key insight is to approach associativity as a confluence property of hypergraph rewrite systems. This approach allows us to define a notion of ternary category and heapoid, where morphisms bind three objects simultaneously, and suggests a systematic study of higher arity forms of associativity.
