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.

中文翻译：

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数论、物理学和拓扑学中的三个 Hopf 代数及其共同背景 II：一般分类公式

我们从数论、数学物理和代数拓扑中考虑了三种完全不同的 Hopf 代数设置。这些是用于多个 zeta 值的 Goncharov 的 Hopf 代数，用于重整化的 Connes-Kreimer 的 Hopf 代数，以及由 Baues 构建的用于研究双环空间的 Hopf 代数。我们表明，通过在最终级别考虑简单对象、乘法和费曼范畴，这些例子可以连续统一。这些考虑打开了在一个大型公共框架中对已知结构进行新结构和重新解释的大门，该框架通过示例逐步呈现。在两篇论文的第二部分中，我们给出了一般的分类公式。