Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three Hopf algebras from number theory, physics & topology, and their
  common background II: general categorical formulation   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.

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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: bayes-an