Abstract
We propose the notion of association schemoids generalizing that of association schemes from small categorical points of view. In particular, a generalization of the Bose–Mesner algebra of an association scheme appears as a subalgebra in the category algebra of the underlying category of a schemoid. In this paper, the equivalence between the categories of groupoids and that of thin association schemoids is established. Moreover linear extensions of schemoids are considered. A general theory of the Baues–Wirsching cohomology deduces a classification theorem for such extensions of a schemoid. We also introduce two relevant categories of schemoids into which the categories of schemes due to Hanaki and due to French are embedded, respectively.
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This research was partially supported by a Grant-in-Aid for Scientific Research HOUGA 25610002 from Japan Society for the Promotion of Science.
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Kuribayashi, K., Matsuo, K. Association Schemoids and Their Categories. Appl Categor Struct 23, 107–136 (2015). https://doi.org/10.1007/s10485-013-9327-6
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DOI: https://doi.org/10.1007/s10485-013-9327-6