论文标题
数字理论，物理和拓扑及其共同背景II的三个HOPF代数II：一般分类表述
Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation
论文作者
论文摘要
我们认为，从数字理论，数学物理学和代数拓扑的HOPF代数的三个先验设置是完全不同的设置。这些是Goncharov的Hopf代数，用于多个ZETA值，Connes-Kreimer用于重生的值，以及由Baues构建的HOPF代数，用于研究双环空间。我们表明，这些示例可以通过考虑简单对象，具有乘法的合作对象和Feynman类别的最终级别来依次统一。这些考虑因素为大型共同框架中已知构造的新结构和重新解释打开了大门，该框架逐步呈现了整个示例。在两篇论文的第二部分中，我们提供了一般的分类配方。
We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework which is presented step-by-step with examples throughout. In this second part of two papers, we give the general categorical formulation.
