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Tool and Object

A History and Philosophy of Category Theory

  • Book
  • © 2007

Overview

Authors:
  1. Ralf Krömer

    1. LPHS-Archives Poincaré (UMR7117 CNRS), Université Nancy 2, Nancy Cedex, France

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  • First comprising historical outline of category theory
  • Includes supplementary material: sn.pub/extras

Part of the book series: Science Networks. Historical Studies (SNHS, volume 32)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xxxvi
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  2. Prelude: Poincaré, Wittgenstein, Peirce, and the use of concepts

    Pages 1-38

  3. Category theory in Algebraic Topology

    Pages 39-92

  4. Category theory in Homological Algebra

    Pages 93-160

  5. Category theory in Algebraic Geometry

    Pages 161-191

  6. From tool to object: full-fledged category theory

    Pages 193-234

  7. Categories as sets: problems and solutions

    Pages 235-280

  8. Categorial foundations

    Pages 281-302

  9. Pragmatism and category theory

    Pages 303-316

  10. Back Matter

    Pages 317-367
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Keywords

About this book

Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance.

Reviews

From the reviews:

“Krömer provides a more complete historical study of category theory and its applications from the beginnings to about 1970. … It caught the attention of people interested in conceptual and philosophical issues … . I recommend Krömer’s work highly to anyone who seeks to gain an understanding of category-theoretic mathematics … . an interesting contribution to the historical philosophy of mathematical practice … . the book is more successful as a history. It is well produced, and the English is clear enough … .” (José Ferreirós, Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin, Issue 1, 2010)

Authors and Affiliations

  • LPHS-Archives Poincaré (UMR7117 CNRS), Université Nancy 2, Nancy Cedex, France

    Ralf Krömer

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