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Elementary Categories, Elementary Toposes(Oxford Logic Guides Vol.21) P 278 p. 95

McLarty, Colin 　著

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価格 \43,906（税込）

発行年月	1996年02月
出版社／提供元	Oxford at the Clarendon Press
出版国	イギリス
言語	英語
媒体	冊子
装丁	paper
ページ数／巻数	278 p., many line illus.
ジャンル	洋書／人文科学／哲学・思想／論理学
ISBN	9780198514732
商品コード	0209504861
商品URL	https://kw.maruzen.co.jp/ims/itemDetail.html?itmCd=0209504861

内容

This book covers elementary aspects of category theory and topos theory. It has few mathematical prerequisites and uses categorical methods throughout rather than beginning with set theoretic foundations. It works with key notions such as cartesian closedness, adjunctions, regular categories, and the internal logic of a topos. Full statements and elementary proofs are given for the central theorems, including the fundamental theorem of toposes, the sheafification theorem, and the constriction of Grothendieck toposes over any topos as base. Three chapters discuss applications of toposes in detail, namely to sets, to basic differential geometry, and to recursive analysis.

Introduction; PART I: CATEGORIES: Rudimentary structures in a category; Products, equalizers, and their duals; Groups; Sub-objects, pullbacks, and limits; Relations; Cartesian closed categories; Product operators and others; PART II: THE CATEGORY OF CATEGORIES: Functors and categories; Natural transformations; Adjunctions; Slice categories; Mathematical foundations; PART III: TOPOSES: Basics; The internal language; A soundness proof for topos logic; From the internal language to the topos; The fundamental theorem; External semantics; Natural number objects; Categories in a topos; Topologies; PART IV: SOME TOPOSES: Sets; Synthetic differential geometry; The effective topos; Relations in regular categories; Further reading; Bibliography; Index.