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February, 2019 Phantom Ideals and Cotorsion Pairs in Extriangulated Categories
Tiwei Zhao, Zhaoyong Huang
Taiwanese J. Math. 23(1): 29-61 (February, 2019). DOI: 10.11650/tjm/180504

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.

Citation

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Tiwei Zhao. Zhaoyong Huang. "Phantom Ideals and Cotorsion Pairs in Extriangulated Categories." Taiwanese J. Math. 23 (1) 29 - 61, February, 2019. https://doi.org/10.11650/tjm/180504

Information

Received: 16 August 2017; Revised: 28 April 2018; Accepted: 20 May 2018; Published: February, 2019
First available in Project Euclid: 9 June 2018

zbMATH: 07021717
MathSciNet: MR3909989
Digital Object Identifier: 10.11650/tjm/180504

Subjects:
Primary: 16E30, 18E40, 18G25

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

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Vol.23 • No. 1 • February, 2019
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