Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585311Special Issue Dedicated to Prof. George A. Grätzer20190701On semi weak factorization structures33567660310.29252/cgasa.11.1.33ENAzadehIlaghi-HosseiniDepartment of Pure Mathematics, Faculty of Math and Computer, Shahid Bahonar University of KermanSeyed ShahinMousavi MirkalaiDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran0000-0002-2904-7692NaserHosseiniDepartment of Pure Mathematics, Faculty of Math and Computers, Shahid Bahonar University of Kerman, Kerman, IranJournal Article20171221In this article the notions of semi weak orthogonality and semi weak factorization structure in a category $mathcal X$ are introduced. Then the relationship between semi weak factorization structures and quasi right (left) and weak factorization structures is given. The main result is a characterization of semi weak orthogonality, factorization of morphisms, and semi weak factorization structures by natural isomorphisms.http://cgasa.sbu.ac.ir/article_76603_4b608595da687086c978149f3a596b28.pdf