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A bicategory of decorated cospans
Theory and applications of categories, Tome 32 (2017), pp. 985-1027.

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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.
Publié le :
Classification : 16B50 and 18D35
Keywords: bicategory, decorated cospan, network, symmetric monoidal 
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     author = {Kenny Courser},
     title = {A bicategory of decorated cospans},
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     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a28/}
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Kenny Courser. A bicategory of decorated cospans. Theory and applications of categories, Tome 32 (2017), pp. 985-1027. http://geodesic.mathdoc.fr/item/TAC_2017_32_a28/