Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 11 Special Issue Dedicated to Prof. George A. Grätzer 2019 07 01 On semi weak factorization structures 33 56 76603 10.29252/cgasa.11.1.33 EN Azadeh Ilaghi-Hosseini Department of Pure Mathematics, Faculty of Math and Computer, Shahid Bahonar University of Kerman Seyed Shahin Mousavi Mirkalai Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran Naser Hosseini Department of Pure Mathematics, Faculty of Math and Computers, Shahid Bahonar University of Kerman, Kerman, Iran Journal Article 2017 12 21 In 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. Quasi right (left) factorization structure (semi weak) orthogonality (semi weak) factorization structure https://cgasa.sbu.ac.ir/article_76603_4b608595da687086c978149f3a596b28.pdf