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Elementary Categories, Elementary Toposes

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Synopses & Reviews

Publisher Comments:

The book covers elementary aspects of category theory and topos theory for graduate students in mathematics, computer science, and logic; it has few mathematical prerequisites, and uses categorical methods throughout, rather than beginning with set theoretical foundations. Working with key concepts such as Cartesian closedness, adjunctions, regular categories, and the internal logic of a topos, the book features full statements and elementary proofs for the central theorems, including the fundamental theorem of toposes, the sheafification theorem, and the construction of Grothendieck toposes over any topos as base. Other chapters discuss applications of toposes in detail, namely to sets, to basic differential geometry, and to recursive analysis.

Table of Contents

PART I: Categories


1. Rudimentary structures in a Category


2. Products, Equalizers, and their Duals


3. Groups


4. Sub-Objects, Pullbacks, and Limits


5. Relations


6. Cartesian Closed Categories


7. Product Operators and Others


PART II: The Category of Categories


8. Functors and Categories


9. Natural Transformations


10. Adjunctions


11. Slice Categories


12. Mathematical Foundations


PART III: Toposes


13. Basics


14. The Internal Language


15. A Soundness Proof for Topos Logic


16. From the Internal Language to the Topos


17. The Fundamental Theorem


18. External Semantics


19. Natural Number Objects


20. Categories in a Topos


21. Topologies


PART IV: Some Toposes


22. Sets


23. Synthetic Differential Geometry


24. The Effective Topos


25. Relations in Regular Categories


Product Details

ISBN:
9780191589492
Publisher:
Clarendon Press
Subject:
main_subject
Subject:
all_subjects
Publication Date:
1995
Binding:
ELECTRONIC
Language:
English
Pages:
265

Related Subjects

Computers and Internet » Computers Reference » General
History and Social Science » Linguistics » General
Humanities » Philosophy » General
Humanities » Philosophy » Logic
Reference » Science Reference » General
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Group Theory

Elementary Categories, Elementary Toposes
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Product details 265 pages Oxford University Press, USA - English 9780191589492 Reviews:
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