Pith. sign in

REVIEW 4 cited by

Structured Cospans

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1911.04630 v3 pith:VVA2M7NJ submitted 2019-11-12 math.CT

Structured Cospans

John C. Baez , Kenny Courser This is my paper
classification math.CT
keywords cospansmathsfstructuredcategorynetworksmonoidalsymmetricwhose
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original 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 $L \colon \mathsf{A} \to \mathsf{X}$, 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.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Rewriting Structured Cospans

    math.CT 2020-01 unverdicted novelty 7.0

    Introduces structured cospan grammars with 2-categorical language construction and proves equivalence to discrete grammars for standard network models, generalizing graph transformation results.

  2. Decomposing time-varying data into simple pieces: structured decompositions of narratives

    math.CT 2026-07 conditional novelty 6.5

    Under stated categorical hypotheses, any spined structured-decomposition theory lifts to a temporal theory on persistent narratives, recovering temporal tree-width, complemented tree-width, and tree-independence number.

  3. Dynamical Systems as Functorial Realisations of Abstract Evolution Shapes

    math.CT 2026-07 accept novelty 5.0

    A categorical framework defines dynamical systems as functors from abstract evolution shapes to coefficient categories, with convergence and Lyapunov stability expressed through cosieve filters and sublevel neighbourhoods.

  4. Double Categories of Open Systems: the Cospan Approach

    math.CT 2025-09 conditional novelty 4.0

    Structured and decorated cospan double categories for open systems have an exoskeleton/outer shell structure, and every object in them is a special symmetric Frobenius pseudomonoid.