Duoidal categories, measuring comonoids and enrichment
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Publication:6339960
arXiv2005.01340MaRDI QIDQ6339960
Christina Vasilakopoulou, Ignacio L. López Franco
Publication date: 4 May 2020
Abstract: 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.
Loop space machines and operads in algebraic topology (55P48) Enriched categories (over closed or monoidal categories) (18D20) Coalgebras and comodules; corings (16T15)
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