Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Traced monoidal categories as algebraic structures in $\mathbf{Prof}$   We define a traced pseudomonoid as a pseudomonoid in a monoidal bicategory
equipped with extra structure, giving a new characterisation of Cauchy complete
traced monoidal categories as algebraic structures in $\mathbf{Prof}$, the
monoidal bicategory of profunctors. This enables reasoning about the trace
using the graphical calculus for monoidal bicategories, which we illustrate in
detail. We apply our techniques to study traced $*$-autonomous categories,
proving a new equivalence result between the left $\otimes$-trace and the right
$\unicode{8523}$-trace, and describing a new condition under which traced
$*$-autonomous categories become autonomous.

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The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat