Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structured Cospans   One goal of applied category theory is to better understand networks
appearing throughout science and engineering. Here we introduce "structured
cospans" as a way to study networks with inputs and outputs. Given a functor $L
\colon \mathsf{A} \to \mathsf{X}$, a structured cospan is a diagram in
$\mathsf{X}$ of the form $L(a) \rightarrow x \leftarrow L(b)$. If $\mathsf{A}$
and $\mathsf{X}$ have finite colimits and $L$ is a left adjoint, we obtain a
symmetric monoidal category whose objects are those of $\mathsf{A}$ and whose
morphisms are isomorphism classes of structured cospans. This is a hypergraph
category. However, it arises from a more fundamental structure: a symmetric
monoidal double category where the horizontal 1-cells are structured cospans.
We show how structured cospans solve certain problems in the closely related
formalism of "decorated cospans", and explain how they work in some examples:
electrical circuits, Petri nets, and chemical reaction networks.

25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
3
The categories of this paper are: physics