ニシザワ コウキ   Nishizawa Koki
  西澤 弘毅
   所属   神奈川大学  工学部 情報システム創成学科
    神奈川大学大学院  工学研究科 工学専攻(情報システム創成領域)
   職種   准教授
言語種別 英語
発行・発表の年月 2022/06
形態種別 学術雑誌
査読 査読あり
標題 Stone dualities from opfibrations
執筆形態 共著
掲載誌名 Journal of Logical and Algebraic Methods in Programming
掲載区分国外
出版社・発行元 Elsevier
巻・号・頁 127(100773),pp.1-19
著者・共著者 Koki Nishizawa, Shin-ya Katsumata, Yuichi Komorida
概要 Stone dualities are dual equivalences between certain categories of algebras and those of topological spaces. A Stone duality is often derived from a dual adjunction between such categories by cutting down unnecessary objects. This dual adjunction is called the fundamental adjunction of the duality, but building it often requires concrete topological arguments. The aim of this paper is to construct fundamental adjunctions generically using (op)fibered category theory. This paper defines an abstract notion of formal spaces (including ordinary topological spaces as the leading example), and gives a construction of a fundamental adjunction between the category of algebras and the category of corresponding formal spaces. Moreover, prove an Adjoint Lifting Theorem in the setting of near 2-fibrations, and construct the fundamental adjunction of Priestley duality.