Construction of Grothendieck categories with enough compressible objects using colored quivers

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Kanda, Ryo¹ 

[1] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan

关键词: Grothendieck category;    Atom spectrum;    Gabriel spectrum;    Colored quiver;    Partially ordered set;   

DOI  :  10.1016/j.jpaa.2019.04.014

来源: Elsevier

【 摘 要 】

We introduce a new method to construct a Grothendieck category from a given colored quiver. This is a variant of the construction used to prove that every partially ordered set arises as the atom spectrum of a Grothendieck category. Using the new method, we prove that for every finite partially ordered set, there exists a locally noetherian Grothendieck category such that every nonzero object contains a compressible subobject and its atom spectrum is isomorphic to the given partially ordered set. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free