Elementary categories, elementary toposes

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Author(s): MacLarty, Colin
Series: Oxford logic guides 21
Edition: Reprint
Publisher: Oxford University Press,Clarendon Press
Year: 1992

Language: English
Pages: 265
City: Oxford
Tags: Kategorie (Mathematik);Topos (Mathematik);Categories (Mathematics);Linear algebra;Toposes

Content: 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 internallanguage 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.