Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bimodule herds   The notion of a bimodule herd is introduced and studied. A bimodule herd
consists of a $B$-$A$ bimodule, its formal dual, called a pen, and a map,
called a shepherd, which satisfies untiality and coassociativity conditions. It
is shown that every bimodule herd gives rise to a pair of corings and
coactions. If, in addition, a bimodule herd is tame i.e. it is faithfully flat
and a progenerator, then these corings are associated to entwining structures;
the bimodule herd is a Galois comodule of these corings. The notion of a
bicomodule coherd is introduced as a formal dualisation of the definition of a
bimodule herd. Every bicomodule coherd defines a pair of (non-unital) rings. It
is shown that a tame $B$-$A$ bimodule herd defines a bicomodule coherd, and
sufficient conditions for the derived rings to be isomorphic to $A$ and $B$ are
discussed. The composition of bimodule herds via the tensor product is
outlined. The notion of a bimodule herd is illustrated by the example of Galois
co-objects of a commutative, faithfully flat Hopf algebra.

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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex