Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Compositional Framework for Bond Graphs   Electrical circuits made only of perfectly conductive wires can be seen as
partitions between finite sets. These are also known as "corelations" and are
the morphisms in the category $\mathrm{FinCorel}$. The two-element set has two
different Frobenius monoid structures in $\mathrm{FinCorel}$. These two
Frobenius monoids are related to "series" and "parallel" junctions, which are
used to connect pairs of wires. We show that these Frobenius monoids interact
to form a "weak bimonoid" as defined by Pastro and Street. We conjecture a
presentation for the subcategory of $\mathrm{FinCorel}$ generated by the
morphisms associated to these two Frobenius monoids, which we call
$\mathrm{FinCorel}^{\circ}$. We are interested in "bond graphs," which are
built from series and parallel junctions. Although the morphisms of
$\mathrm{FinCorel}^{\circ}$ resemble bond graphs, there is not a perfect
correspondence. Since bond graphs and circuits determine Lagrangian relations
between symplectic vector spaces, we then consider the category of Lagrangian
relations, $\mathrm{LagRel}_k$. Bond graphs pick out a subcategory
$\mathrm{LagRel}_k^{\circ}$ with generating morphisms corresponding to those of
$\mathrm{FinCorel}^{\circ}$. Thus we define a category $\mathrm{BondGraph}$
with generators and equations that are found in both
$\mathrm{FinCorel}^{\circ}$ and $\mathrm{LagRel}_k^{\circ}$. We study the
functorial semantics of $\mathrm{BondGraph}$ by giving two different functors
from it to the category $\mathrm{LagRel}_k$ and a natural transformation
between them. Given a bond graph, the first functor picks out a Lagrangian
relation in terms of "effort" and "flow," while the second picks one out in
terms of "potential" and "current." The natural transformation arises from the
way that effort and flow relate to potential and current.

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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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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: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin