On Mitchell's embedding theorem for a quasi-schemoid

JOURNAL OF ALGEBRA

卷:458

Article

Kuribayashi, Katsuhiko¹  Momose, Yasuhiro¹ 

[1] Shinshu Univ, Fac Sci, Dept Math Sci, Matsumoto, Nagano 3908621, Japan

关键词: Schemoid;    Functor category;    Model category;    Morita equivalence;   

DOI  :  10.1016/j.jalgebra.2016.03.019

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free