Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The relative modular object and Frobenius extensions of finite Hopf
  algebras   For a certain kind of tensor functor $F: \mathcal{C} \to \mathcal{D}$, we
define the relative modular object $\chi_F \in \mathcal{D}$ as the "difference"
between a left adjoint and a right adjoint of $F$. Our main result claims that,
if $\mathcal{C}$ and $\mathcal{D}$ are finite tensor categories, then $\chi_F$
can be written in terms of a categorical analogue of the modular function on a
Hopf algebra. Applying this result to the restriction functor associated to an
extension $A/B$ of finite-dimensional Hopf algebras, we recover the result of
Fischman, Montgomery and Schneider on the Frobenius type property of $A/B$. We
also apply our results to obtain a "braided" version and a "bosonization"
version of the result of Fischman et al.

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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: q-fin