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arXiv · 1611.00477

Phantom ideals and cotorsion pairs in extriangulated categories

Tiwei Zhao·Zhaoyong Huang
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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 $(\C,\E,\s)$ 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.

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Tiwei Zhao, Zhaoyong Huang. 2017-02-14. Phantom ideals and cotorsion pairs in extriangulated categories. https://arxiv.org/abs/1611.00477

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