Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the structure of cofree Hopf algebras   We prove an analogue of the Poincare'-Birkhoff-Witt theorem and of the
Cartier-Milnor-Moore theorem for non-cocommutative Hopf algebras. The primitive
part of a cofree Hopf algebra is a B-infini-algebra. We construct a universal
enveloping functor U2 from B-infini-algebras to 2-associative algebras, i.e.
algebras equipped with two associative operations. We show that any cofree Hopf
algebra H is of the form U2(Prim H). We take advantage of the simple
description of the free 2as-algebra in terms of planar trees to unravel the
structure of the operad B-infini.

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The categories of this paper are: physics
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The categories of this paper are: nlin
30
The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex