DECORATED COSPANS

作者：Fong Brendan^*

来源：Theory and Applications of Categories, 2015, 30: 1096-1120.

• cospan
• decorated cospan
• hypergraph category
• well-supported compact closed category
• separable algebra
• Frobenius algebra
• Frobenius monoid

Let C be a category with finite colimits, writing its coproduct +, and let (D, circle times) be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided monoidal functor F: (C,+) (D, circle times), 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 -> N <- Y in C together with an element 1 -> 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.

• 出版日期2015