关于拟模式的Mitchell嵌入定理
On Mitchell's embedding theorem for a quasi-schemoid
摘要：
拟模式是一个小范畴，它的态射被适当的组合数据着色。本文建立了Tame模式的Mitchell嵌入定理。这个结果使我们能够给出以模为定义域的函子范畴上的链复形范畴的一个上纤生成的模型范畴结构。此外，还引入了模类的Morita等价的概念，并对它进行了讨论.特别地，我们证明了二进制码的每一个Hamming方案都与二阶循环群的结合方案Morita等价。在附录中，我们从一个抽象的单纯复形构造了一个新的模式，它的Bose-Mesner代数与给定复形的Stanley-Reisner环密切相关。
英文摘要：
A quasi-schemoid is a small category whose morphisms are colored with appropriate combinatorial data. In this note, 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.
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