2020/05/04 by Ignacio López Franco, Christina Vasilakopoulou, Franco, Ignacio López +1
Mathematics · #18D10 #18D20 (Primary) 16T15 #18D50 #55P48 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2005.01340
openalex publication_date 2020/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the theory of Sweeder's measuring comonoids to the framework of duoidal categories: categories equipped with two compatible monoidal structures. We use one of the tensor products to endow the category of monoids for the other with an enrichment in the category of comonoids. The enriched homs are provided by the universal measuring comonoids. We study a number of duoidal structures on categories of graded objects and of species and the associated enriched categories, such as an enrichment of graded (twisted) monoids in graded (twisted) comonoids, as well as two enrichments of symmetric operads in symmetric cooperads.