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arxiv: 2207.13465 · v1 · pith:U3XFTT7Tnew · submitted 2022-07-27 · 🧮 math.CT

Ideal approximation in n-exangulated categories

classification 🧮 math.CT
keywords idealapproximationcategoryexangulatedmathcalmathscralmostassociated
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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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  1. $n$-Extension closed subcategories of $n$-exangulated categories

    math.RT 2022-09 unverdicted novelty 5.0

    n-extension closed subcategories inherit n-exangulated structure; n-exact categories are characterized as n-exangulated categories with monic inflations and epic deflations; (WIC) equivalent to weakly idempotent compl...