Thick Subcategories of Extriangulated Categories

Abstract

We introduce the spectrum of an extriangulated category with respect to a class of thick subcategories as well as supports of thick subcategories. Then we give a classification of radical thick subcategories of an extriangulated category in terms of supports of thick subcategories. Moreover, we introduce the notions of prime thick subcategories and classifying support data, and show that if (X, σ) is a classifying support data on an extriangulated category $\cal{K}$, then there is a homeomorphism from the topological space X to the spectrum of $\cal{K}$ with respect to the set of prime thick subcategories. This result generalizes a result of Matsui.

Keywords

Extriangulated categories / thick subcategories / spectra / supports / radical thick subcategories / prime thick subcategories / 18G25 / 18G80 / 18F60

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Peking University

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