Elementary Categories, Elementary Toposes

Häftad, Engelska, 1995

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Beskrivning

The 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 construction 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.

Produktinformation

Utgivningsdatum:1995-04-27
Mått:155 x 233 x 16 mm
Vikt:429 g
Format:Häftad
Språk:Engelska
Serie:Oxford Logic Guides
Antal sidor:278
Förlag:Clarendon Press
ISBN:9780198514732

Utforska kategorier

Matematikens grunder inom Naturvetenskap och teknik

Recensioner i media

It has the virtue of bringing together a great deal of basic material which is otherwise scattered about in research texts and articles.

Innehållsförteckning

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.