Two monads on the category of graphs
classification
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keywords
categorycategoriesgraphsmatchingsmonadspartialperfectsteiner
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We introduce two monads on the category of graphs and prove that their Eilenberg-Moore categories are isomorphic to the category of perfect matchings and the category of partial Steiner triple systems, respectively. As a simple application of these results, we describe the product in the categories of perfect matchings and partial Steiner triple systems.
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