2022-05-18T07:54:10Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000190512021-09-02T06:24:05Z1169:1170On Mitchell's embedding theorem for a quasi-schemoidKuribayashi, Katsuhiko© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/SchemoidFunctor categoryModel categoryMorita equivalenceA quasi-schemoid is a small category whose morphisms are colored with appropriate combinatorial data. In this paper, Mitchell's embeddingtheorem 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.ArticleJOURNAL OF ALGEBRA. (458):222-248 (2016)ACADEMIC PRESS INC ELSEVIER SCIENCE2016-07-15engjournal articleAMhttp://hdl.handle.net/10091/00019813https://soar-ir.repo.nii.ac.jp/records/19051https://doi.org/10.1016/j.jalgebra.2016.03.01910.1016/j.jalgebra.2016.03.0190021-8693AA00692420JOURNAL OF ALGEBRA458222248https://soar-ir.repo.nii.ac.jp/record/19051/files/25610002_01.pdfapplication/pdf209.0 kB2016-07-18