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The category of simple graphs is coreflective in the comma category of groups under the free group functor

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 نشر من قبل Christian Frank
 تاريخ النشر 2021
  مجال البحث
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 تأليف Christian Frank




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We show that the comma category $(mathcal{F}downarrowmathbf{Grp})$ of groups under the free group functor $mathcal{F}: mathbf{Set} to mathbf{Grp}$ contains the category $mathbf{Gph}$ of simple graphs as a full coreflective subcategory. More broadly, we generalize the embedding of topological spaces into Steven Vickers category of topological systems to a simple technique for embedding certain categories into comma categories, then show as a straightforward application that simple graphs are coreflective in $(mathcal{F}downarrowmathbf{Grp})$.



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