Geodesic
Structured cospans
Theory and applications of categories, Tome 35 (2020), pp. 1771-1822

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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: A -> X, a structured cospan is a diagram in X of the form L(a) -> x <- L(b). If A and X have finite colimits and L is a left adjoint, we obtain a symmetric monoidal category whose objects are those of 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.

Publié le :
Classification : 18B10, 18M35, 18N10
Keywords: bicategory, cospan, double category, monoidal category, network 
@article{TAC_2020_35_a47,
     author = {John C. Baez and Kenny Courser},
     title = {Structured cospans},
     journal = {Theory and applications of categories},
     pages = {1771--1822},
     publisher = {mathdoc},
     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a47/}
}
TY  - JOUR
AU  - John C. Baez
AU  - Kenny Courser
TI  - Structured cospans
JO  - Theory and applications of categories
PY  - 2020
SP  - 1771
EP  - 1822
VL  - 35
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2020_35_a47/
LA  - en
ID  - TAC_2020_35_a47
ER  - 
%0 Journal Article
%A John C. Baez
%A Kenny Courser
%T Structured cospans
%J Theory and applications of categories
%D 2020
%P 1771-1822
%V 35
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2020_35_a47/
%G en
%F TAC_2020_35_a47
John C. Baez; Kenny Courser. Structured cospans. Theory and applications of categories, Tome 35 (2020), pp. 1771-1822. http://geodesic.mathdoc.fr/item/TAC_2020_35_a47/