Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Categorified trace for module tensor categories over braided tensor
  categories   Given a braided pivotal category $\mathcal C$ and a pivotal module tensor
category $\mathcal M$, we define a functor $\mathrm{Tr}_{\mathcal C}:\mathcal M
\to \mathcal C$, called the associated categorified trace. By a result of
Bezrukavnikov, Finkelberg and Ostrik, the functor $\mathrm{Tr}_{\mathcal C}$
comes equipped with natural isomorphisms $\tau_{x,y}:\mathrm{Tr}_{\mathcal C}(x
\otimes y) \to \mathrm{Tr}_{\mathcal C}(y \otimes x)$, which we call the
traciators. This situation lends itself to a diagramatic calculus of `strings
on cylinders', where the traciator corresponds to wrapping a string around the
back of a cylinder. We show that $\mathrm{Tr}_{\mathcal C}$ in fact has a much
richer graphical calculus in which the tubes are allowed to branch and braid.
Given algebra objects $A$ and $B$, we prove that $\mathrm{Tr}_{\mathcal C}(A)$
and $\mathrm{Tr}_{\mathcal C}(A \otimes B)$ are again algebra objects.
Moreover, provided certain mild assumptions are satisfied,
$\mathrm{Tr}_{\mathcal C}(A)$ and $\mathrm{Tr}_{\mathcal C}(A \otimes B)$ are
semisimple whenever $A$ and $B$ are semisimple.

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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol