Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bicovariant Differential Calculi and Cross Products on Braided Hopf
  Algebras   We consider Hopf bimodules and crossed modules over a Hopf algebra $H$ in a
braided category. They are the key-stones for braided bicovariant differential
calculi and their invariant vector fields respectively, as well as for the
construction of braided Hopf algebra cross products. We show that the notions
of Hopf bimodules and crossed modules are equivalent. A generalization of the
Radford-Majid criterion to the braided case is given and it is seen that
bialgebra cross products over the Hopf algebra $H$ are precisely described by
$H$-crossed module bialgebras. We study the theory of (bicovariant)
differential calculi in braided abelian categories and we construct
$\NN_0$-graded bicovariant differential calculi out of first order bicovariant
differential calculi. These objects are shown to be Hopf algebra differential
calculi with universal bialgebra properties in the braided $\NN_0$-graded
category.

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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn