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arXiv · 2207.13465

Ideal approximation in $n$-exangulated categories

Yucheng Wang·Jiaqun Wei
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Abstract

In this paper, we study the ideal approximation theory associated to almost $n$-exact structures in the $n$-exangulated category. The notions of $n$-ideal cotorsion pairs and $n$-$\mathbb{F}$-phantom morphisms are introduced and studied. In particular, let $\mathscr{C}$ be an extriangulated category which satisfies the condition (WIC) and $\mathcal{T}$ be a nicely embedded $n$-cluster tilting subcategory of $\mathscr{C}$, we prove Salce's Lemma in $\mathcal{T}$.

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Yucheng Wang, Jiaqun Wei. 2022-07-27. Ideal approximation in $n$-exangulated categories. https://arxiv.org/abs/2207.13465

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