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arXiv · 2010.04393

Semibricks in extriangulated categories

Li Wang·Jiaqun Wei·Haicheng Zhang
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Abstract

Let $\mathcal{X}$ be a semibrick in an extriangulated category $\mathscr{C}$. Let $\mathcal{T}$ be the filtration subcategory generated by $\mathcal{X}$. We give a one-to-one correspondence between simple semibricks and length wide subcategories in $\mathscr{C}$. This generalizes a bijection given by Ringel in module categories, which has been generalized by Enomoto to exact categories. Moreover, we also give a one-to-one correspondence between cotorsion pairs in $\mathcal{T}$ and certain subsets of $\mathcal{X}$. Applying to the simple minded systems of an triangulated category, we recover a result given by Dugas.

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Li Wang, Jiaqun Wei, Haicheng Zhang. 2020-10-09. Semibricks in extriangulated categories. https://arxiv.org/abs/2010.04393

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