Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invertible Bimodules, Miyashita Action in Monoidal Categories and
  Azumaya Monoids   In this paper we introduce and study Miyashita action in the context of
monoidal categories aiming by this to provide a common framework of previous
studies in the literature. We make a special emphasis of this action on Azumaya
monoids. To this end, we develop the theory of invertible bimodules over
different monoids (a sort of Morita contexts) in general monoidal categories as
well as their corresponding Miyashita action. Roughly speaking, a Miyashita
action is a homomorphism of groups from the group of all isomorphic classes of
invertible subobjects of a given monoid to its group of automorphisms. In the
symmetric case, we show that for certain Azumaya monoids, which are abundant in
practice, the corresponding Miyashita action is always an isomorphism of
groups. This generalizes Miyashita's classical result and sheds light on other
applications of geometric nature which can not be treated using the classical
theory. In order to illustrate our methods, we give a concrete application to
the category of comodules over commutative (flat) Hopf algebroids. This
obviously includes the special cases of split Hopf algebroids (action
groupoids), which for instance cover the situation of the action of an affine
algebraic group on an affine algebraic variety.

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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol