On Mitchell's embedding theorem for a quasi-schemoid

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• 作者：Katsuhiko Kuribayashi ; ^{kuri@math.shinshu-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Yasuhiro Momose ^{momose@math.shinshu-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05E30 ; 16D90 ; 18D35 ; 18E30
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 July 2016
• 年：2016
• 卷：458
• 期：Complete
• 页码：222-248
• 全文大小：510 K

文摘

A quasi-schemoid is a small category whose morphisms are colored with appropriate combinatorial data. In this paper, Mitchell's embedding theorem for a tame schemoid is established. The result allows us to give a cofibrantly generated model category structure to the category of chain complexes over a functor category with a schemoid as the domain. Moreover, a notion of Morita equivalence for schemoids is introduced and discussed. In particular, we show that every Hamming scheme of binary codes is Morita equivalent to the association scheme arising from the cyclic group of order two. In an appendix, we construct a new schemoid from an abstract simplicial complex, whose Bose–Mesner algebra is closely related to the Stanley–Reisner ring of the given complex.