{"title":"机架交叉模块类别的完备性","authors":"Hatice GÜLSÜN AKAY, I. Akça","doi":"10.54286/ikjm.1199290","DOIUrl":null,"url":null,"abstract":"In this paper, we prove that the category of rack crossed modules (with a fixed codomain) is finitely complete. In other words, we construct the product, pullback and equalizer objects in the category of crossed modules of racks. We therefore unify the group-theoretical analogy of the completeness property in the sense of the functor $\\mathbf{Conj \\colon Grp \\to Rack} $.","PeriodicalId":114258,"journal":{"name":"Ikonion Journal of Mathematics","volume":"178 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Completeness of the Category of Rack Crossed Modules\",\"authors\":\"Hatice GÜLSÜN AKAY, I. Akça\",\"doi\":\"10.54286/ikjm.1199290\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we prove that the category of rack crossed modules (with a fixed codomain) is finitely complete. In other words, we construct the product, pullback and equalizer objects in the category of crossed modules of racks. We therefore unify the group-theoretical analogy of the completeness property in the sense of the functor $\\\\mathbf{Conj \\\\colon Grp \\\\to Rack} $.\",\"PeriodicalId\":114258,\"journal\":{\"name\":\"Ikonion Journal of Mathematics\",\"volume\":\"178 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ikonion Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.54286/ikjm.1199290\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ikonion Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.54286/ikjm.1199290","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Completeness of the Category of Rack Crossed Modules
In this paper, we prove that the category of rack crossed modules (with a fixed codomain) is finitely complete. In other words, we construct the product, pullback and equalizer objects in the category of crossed modules of racks. We therefore unify the group-theoretical analogy of the completeness property in the sense of the functor $\mathbf{Conj \colon Grp \to Rack} $.