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arXiv · 1607.06529

Phantom covering ideals in categories without enough projective morphisms

Sergio Estrada·Pedro A. Guil Asensio·Sinem Odabasi
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Abstract

We give sufficient conditions to ensure that the ideal $\Phi(\mathcal E)$ of $\mathcal E$-phantom maps in a locally $\lambda$-presentable exact category $(\mathcal{A}, \mathcal{E})$ is (special) (pre)covering ideal, where $\mathcal E$ is an exact substructure of $(\mathcal{A}, \mathcal{E})$. As a byproduct, we infer the existence of various covering ideals in categories of sheaves which have a meaningful geometrical motivation. In particular we deal with a Zariski-local notion of phantom maps in categories of sheaves. We would like to point out that our approach is necessarily different from [FGHT13], as the categories involved in most of the examples we are interested in do not have enough projective morphisms.

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BibTeXRIS

Sergio Estrada, Pedro A. Guil Asensio, Sinem Odabasi. 2016-07-21. Phantom covering ideals in categories without enough projective morphisms. https://arxiv.org/abs/1607.06529

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