Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hopf (Bi-)Modules and Crossed Modules in Braided Monoidal Categories   Hopf (bi-)modules and crossed modules over a bialgebra B in a braided
monoidal category C are considered. The (braided) monoidal equivalence of both
categories is proved provided B is a Hopf algebra (with invertible antipode).
Bialgebra projections and Hopf bimodule bialgebras over a Hopf algebra in C are
found to be isomorphic categories. As a consequence a generalization of the
Radford-Majid criterion for a braided Hopf algebra to be a cross product is
obtained. The results of this paper turn out to be fundamental for the
construction of (bicovariant) differential calculi on braided Hopf algebras.

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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: chem-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