On Mitchell's embedding theorem for a quasi-schemoid
On Mitchell's embedding theorem for a quasi-schemoid
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关于拟 Schoid 的 Mitchell 嵌入定理
DOI：
10.1016/j.jalgebra.2016.03.019
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发表时间：
2016
影响因子：
0.9
通讯作者：
Katsuhiko Kuribayashi and Yasuhiro Momose
中科院分区：
文献类型：
--
作者：
Maki Sachiko;Eiji Nishibori;Masanori Yoshida;Shinobu Aoyagi;Makoto Sakata;Masaki Takata;Mio Kondo;Masaki Murata;Ryota Sakamoto;Hiroshi Nishihara;S.Maki;畠山あかり，西堀英治，Lei Miao，木村薫，高田昌樹;E. Nishibori and H. Kasai,;Eiji Nishibori;Eiji Nishibori;Eiji Nishibori;Eiji Nishibori;西堀英治;Katsuhiko Kuribayashi and Yasuhiro Momose
拟模式是一个小类别，其态射用适当的组合数据着色。本文建立了atameschemoid的Mitchell嵌入定理。结果使我们能够为以 schemoid 作为域的函子类别上的链复合体类别提供共纤维生成的模型类别结构。此外，还介绍并讨论了 schemoid 的 Morita 等价概念。特别是，我们证明了二进制码的每个汉明方案都是 Morita 等价于二阶循环群产生的关联方案。在附录中，我们从抽象单纯复形构造了一个新的拟图，其 Bose-Mesner 代数与给定复形的 Stanley-Reisner 环密切相关。
A quasi-schemoid is a small category whose morphisms are colored with appropriate combinatorial data. In this paper, Mitchell's embedding theorem for atameschemoid 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.