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- W2963351767 abstract "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 $(mathscr{C},mathbb{E},mathfrak{s})$ 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 $mathscr{C}$; (2) special preenveloping ideals of $mathscr{C}$; (3) additive subfunctors of $mathbb{E}$ having enough special injective morphisms; and (4) additive subfunctors of $mathbb{E}$ having enough special projective morphisms. Moreover, we show that if $(mathscr{C},mathbb{E}, mathfrak{s})$ 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 $mathscr{C}$; (2) all additive subfunctors of $mathbb{E}$ having enough special injective objects." @default.
- W2963351767 created "2019-07-30" @default.
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- W2963351767 date "2019-02-01" @default.
- W2963351767 modified "2023-10-16" @default.
- W2963351767 title "Phantom Ideals and Cotorsion Pairs in Extriangulated Categories" @default.
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- W2963351767 doi "https://doi.org/10.11650/tjm/180504" @default.
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