2016/11/02 by Tiwei Zhao, Zhao, Tiwei, Zhaoyong Huang +1
Mathematics · #16E30 #18E40 #18G25 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings, Modules, and Algebras #math.CT #math.RT #msc:16E30 #msc:18E40 #msc:18G25
paper · pdf · doi:10.48550/arxiv.1611.00477
29 pages, the introduction is re-organized and examples 2.8 and 3.2 are added
openalex publication_date 2016/11/02 · arxiv created 2017/02/14 · arxiv updated 2017/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce and study relative phantom morphisms in extriangulated categories defined by Nakaoka and Palu. Then using their properties, we show that if (\C,\E,\s) is an extriangulated category with enough injective objects and projective objects, then there exists a bijective correspondence between any two of the following classes: (1) special precovering ideals of \C; (2) special preenveloping ideals of \C; (3) additive subfunctors of \E having enough special injective morphisms; and (4) additive subfunctors of \E having enough special projective morphisms. Moreover, we show that if (\C,\E,\s) is an extriangulated category with enough injective objects and projective morphisms, then there exists a bijective correspondence between the following two classes: (1) all object-special precovering ideals of \C; (2) all additive subfunctors of \E having enough special injective objects.