#
A bicategory of decorated cospans

##
Kenny Courser

If C is a category with pullbacks then there is a bicategory with the same
objects as 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 C equipped with extra structure. This extra structure
arises from a symmetric lax monoidal functor F : C --> D; we use this
functor to `decorate' each cospan with apex N in C with an element of
F(N). Using a result of Shulman, we show that when C has finite colimits,
decorated cospans are morphisms in a symmetric monoidal bicategory. We
illustrate our construction with examples from electrical engineering and
the theory of chemical reaction networks.

Keywords:
bicategory, decorated cospan, network, symmetric monoidal

2010 MSC:
16B50 and 18D35

*Theory and Applications of Categories,*
Vol. 32, 2017,
No. 29, pp 985-1027.

Published 2017-08-17.

http://www.tac.mta.ca/tac/volumes/32/29/32-29.pdf

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