Logic, Epistemology, and the Unity of Science

From a Geometrical Point of View

A Study of the History and Philosophy of Category Theory

Authors: Marquis, Jean-Pierre

  • Provides a conceptual introduction to the fundamental concepts of category theory and categorical logic
  • Gives a unique perspective on the nature of category theory and its role in mathematics and its foundations
  • Gives insights into the historical development of the field
  • Brings together historical, mathematical and philosophical considerations
see more benefits

Buy this book

eBook $209.00
price for USA (gross)
  • ISBN 978-1-4020-9384-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $269.00
price for USA
  • ISBN 978-1-4020-9383-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $269.00
price for USA
  • ISBN 978-90-481-8117-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein’s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane’s work in the early 1940’s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics.

From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.

About the authors

Jean-Pierre Marquis teaches logic, epistemology and philosophy of science at the Université de Montréal. He has published papers on category theory, categorical logic, general philosophy of mathematics and philosophy of science.

Reviews

From the reviews:

"The main and basic point is that category theory is thoroughly geometric. … The monograph is highly readable, and it should be valuable to every expert in category theory, every novice in category theory and every mathematician who is not interested at all in category theory." (Hirokazu Nishimura, Zentralblatt MATH, Vol. 1165, 2009)

“The creation of a book such as this marks an interesting point in the history and philosophy of category theory. … While reading the book, I used the opportunity to revisit several seminal papers and to marvel at the advances they represented. The author clearly studied each paper thoroughly, had private communications with some pioneers, and succeeded quite well in describing the mathematical community’s mind set at the time of those advances. … I conclude by recommending the book.” (R. H. Street, Mathematical Reviews, Issue 2012 d)


Table of contents (9 chapters)

  • Introduction

    Marquis, Jean-Pierre

    Pages 1-8

  • Category Theory and Klein’s Erlangen Program

    Marquis, Jean-Pierre

    Pages 9-40

  • Introducing Categories, Functors and Natural Transformations

    Marquis, Jean-Pierre

    Pages 41-72

  • Categories as Spaces, Functors as Transformations

    Marquis, Jean-Pierre

    Pages 73-108

  • Discovering Fundamental Categorical Transformations: Adjoint Functors

    Marquis, Jean-Pierre

    Pages 109-145

Buy this book

eBook $209.00
price for USA (gross)
  • ISBN 978-1-4020-9384-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $269.00
price for USA
  • ISBN 978-1-4020-9383-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $269.00
price for USA
  • ISBN 978-90-481-8117-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
From a Geometrical Point of View
Book Subtitle
A Study of the History and Philosophy of Category Theory
Authors
Series Title
Logic, Epistemology, and the Unity of Science
Series Volume
14
Copyright
2009
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-9384-5
DOI
10.1007/978-1-4020-9384-5
Hardcover ISBN
978-1-4020-9383-8
Softcover ISBN
978-90-481-8117-9
Series ISSN
2214-9775
Edition Number
1
Number of Pages
X, 310
Topics