Decorated cospans

By Brendan Fong. Theory and Applications of Categories, 2015

79 citations recorded by the source corpus.

Let $\mathcal C$ be a category with finite colimits, writing its coproduct $+$, and let $(\mathcal D, \otimes)$ be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided monoidal functor $F: (\mathcal C,+) \to (\mathcal D, \otimes)$, and of producing a strong monoidal functor between such categories from a monoidal natural transformation between such functors. The objects of these categories, our so-called `decorated cospan categories', are simply the objects of $\mathcal C$, while the morphisms are pairs comprising a cospan $X \rightarrow N \leftarrow Y$ in $\mathcal C$ together with an element $1 \to FN$ in $\mathcal D$. Moreover, decorated cospan categories are multigraph categories---each object is equipped with a special commutative Frobenius monoid---and their functors preserve this structure.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bd603792b4e90a9d0ccc569b3304326d3d47a677

Citations in the corpus

• Monoidal Grothendieck Construction (2018, unknown): “ost-composing with the forgetful to Set which discards morphisms between graphs, we obtain the motivating example in Fong’s so-called theory of decorated cospans MONOIDAL GROTHENDIECK CONSTRUCTION 29 [Fon15].1 In more detail, therein a category FCospanis constructed from a given symmetric lax monoid”