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2016

A bicategory of decorated cospans

Courser, Kenny

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If $\mathbf{C}$ is a category with pullbacks then there is a bicategory with the same objects as $\mathbf{C}$, spans as morphisms, and maps of spans as 2-morphisms, as shown by Benabou.

Fong has developed a theory of "decorated" cospans, which are cospans in $\mathbf{C}$ equipped with extra structure.
This extra structure arises from a lax symmetric monoidal functor $F \colon \mathbf{C} \to \mathbf{D}$; we use this functor to "decorate" each cospan with apex $N \in \mathbf{C}$ with an element of $F(N)$.
Using a result of Shulman, we show that when $\mathbf{C}$ has finite colimits, decorated cospans are morphisms in a symmetric monoidal bicategory.

A bicategory of decorated cospans · Around

Built on

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M. Grandis and R. Pare, Limits in double categories, Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Then

B. Fong, Decorated cospans, Theory and Applications of Categories
Original
2015
Later among the works it cites.
J. C. Baez, B. Fong and B. Pollard, A compositional framework for Markov processes, Jour. Math. Phys
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2016
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B. Pollard, Open Markov processes: A compositional perspective on non-equilibrium steady states in biology, Entropy
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