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    Dear Committee Members

    Julie Schumacher 9780385538138


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Elementary Categories, Elementary Toposes


Elementary Categories, Elementary Toposes Cover


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

Clarendon Press
Publication Date:

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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