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Structured Cospans | | John C. Baez
; Kenny Courser
; | | Date: |
12 Nov 2019 | | Abstract: | 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 $L
colon mathsf{A} o mathsf{X}$, a structured cospan is a diagram in
$mathsf{X}$ of the form $L(a)
ightarrow x leftarrow L(b)$. 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. | | Source: | arXiv, 1911.4630 | | Services: | Forum | Review | PDF | Favorites | |
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