Decorated cospans

Brendan Fong

Theory and applications of categories, Tome 30 (2015), pp. 1096-1120

Résumé

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

Détail

Publié le : 2015-08-06

Classification : 18C10, 18D10
Keywords: cospan, decorated cospan, hypergraph category, well-supported compact closed category, separable algebra, Frobenius algebra, Frobenius monoid