2024/11/06 by James Cranch, Cranch, James, Georg Struth +1 · 2 citations
Engineering · Materials Science · #06A12 #18D10 #68Q85 #Advanced Materials and Mechanics #Category Theory (math.CT) #Diatoms and Algae Research #FOS: Computer and information sciences #FOS: Mathematics #Logic in Computer Science (cs.LO) #Modular Robots and Swarm Intelligence
paper · pdf · doi:10.48550/arxiv.2411.03821
openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
With a view on applications in computing, in particular concurrency theory and higher-dimensional rewriting, we develop notions of n-fold monoid and comonoid objects in n-fold monoidal categories and bicategories. We present a series of examples for these structures from various domains, including a categorical model for a communication protocol and a lax n-fold relational monoid, which has previously been used implicitly for higher-dimensional rewriting and which specialises in a natural way to strict n-categories. A special set of examples is built around modules and algebras of the boolean semiring, which allows us to deal with semilattices, additively idempotent semirings and quantales using tools from classical algebra.