Hypergraph Categories — Brendan Fong & David I Spivak (2018). arXiv:1806.08304 (v3, PDF).
Studies hypergraph categories — symmetric monoidal categories with a coherent special commutative Frobenius structure on every object — and shows they are equivalent to algebras over cospan operads (‘cospan-algebras’). Proves that every hypergraph category is self-dual compact closed and that cospans form the free hypergraph category.
Sources: the paper, arXiv:1806.08304v3, checked against the arXiv listing. Index: Papers.
Key definitions and results
- Definition 2.5: special commutative Frobenius monoid
- Definition 2.12: hypergraph category
- Proposition 3.1: hypergraph categories are self-dual compact closed
- Proposition 3.8: Cospan is the theory of special commutative Frobenius monoids
- Theorem 3.14: is the free hypergraph category
Concept notes
Hypergraph Category, Frobenius Monoid, Compact Closed Category, Cospan