Overview
- 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
- The only book weaving together historical, mathematical and philosophical considerations
Part of the book series: Logic, Epistemology, and the Unity of Science (LEUS, volume 14)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
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.
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)
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: From a Geometrical Point of View
Book Subtitle: A Study of the History and Philosophy of Category Theory
Authors: Jean-Pierre Marquis
Series Title: Logic, Epistemology, and the Unity of Science
DOI: https://doi.org/10.1007/978-1-4020-9384-5
Publisher: Springer Dordrecht
eBook Packages: Humanities, Social Sciences and Law, Philosophy and Religion (R0)
Copyright Information: Springer Science+Business Media B.V. 2009
Hardcover ISBN: 978-1-4020-9383-8Published: 08 January 2009
Softcover ISBN: 978-90-481-8117-9Published: 28 October 2010
eBook ISBN: 978-1-4020-9384-5Published: 20 November 2008
Series ISSN: 2214-9775
Series E-ISSN: 2214-9783
Edition Number: 1
Number of Pages: X, 310
Topics: Philosophy of Science, History of Mathematical Sciences, Category Theory, Homological Algebra, Mathematical Logic and Foundations, Algebraic Topology