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Duoidal categories, measuring comonoids and enrichment

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arxiv 2005.01340 v1 pith:EYPQUH45 submitted 2020-05-04 math.CT

Ignacio López Franco , Christina Vasilakopoulou This is my paper · ORCID
classification math.CT
keywords categoriescomonoidsduoidalenrichmentgradedmeasuringcategoryenriched
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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.

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  1. The category of necklaces is a test category

    math.CT 2026-07 accept novelty 6.0 of 10

    The category of necklaces is a test category, so its presheaf category is a model for homotopy types.

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