自由非对称操作元的诺特形式
Noetherian forms of free non-symmetric operads
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中文总结 AI 辅助
本文研究带标签有限有根有序树范畴，通过正合性性质刻画其同构类，并证明附加严格初始对象后具有诺特形式。
中文摘要 AI 辅助
本文研究固定标签集合上的带标签有限有根有序树范畴，其中每个标签配备一个元数：即具有该标签的顶点必须拥有的固定子节点数。等价地，这些是自由非对称操作元中运算的表达式树。这些树之间的态射将一棵树的修剪（前缀）与另一棵树的整个子树（后缀）相匹配。我们利用适当的正合性性质，在同构意义下刻画了此类范畴。结果表明，这些范畴表现出强代数行为，即每个此类范畴在附加严格初始对象后，都具有特别良好的诺特形式。
英文摘要
In this paper, we study certain categories of labeled finite rooted ordered trees over a fixed set of labels where each label is equipped with an arity: a fixed number of children that the vertex with the given label must have. Equivalently, these are expression trees for operations in a free non-symmetric operad. A morphism between these trees matches a pruning of one tree (a prefix) with an entire subtree of another (a suffix). We characterize such categories, up to isomorphism, in terms of suitable exactness properties. It turns out that these categories exhibit strong algebraic behavior, in the sense that every such category, when appended with a strict initial object, has a particularly nice noetherian form.
发表机构
- Mathematics Division, Department of Mathematical Sciences（数学系）
- Stellenbosch University（斯坦伦布什大学）
- National Institute for Theoretical and Computational Sciences (NITheCS)（国家理论与计算科学研究所）
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