From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory (Logic, Epistemology, and the Unity of Science)
| Author | : | |
| Rating | : | 4.92 (744 Votes) |
| Asin | : | 1402093837 |
| Format Type | : | paperback |
| Number of Pages | : | 310 Pages |
| Publish Date | : | 2018-01-27 |
| Language | : | English |
DESCRIPTION:
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.
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. 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 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 read
… I conclude by recommending the book.” (R. Street, Mathematical Reviews, Issue 2012 d). … 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. H. From the reviews:"The main and basic point is that category theory is thoroughly geometric. 1165, 2009)“The creation of a book such as this marks an interesting point in the history and philosophy of category theory. 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. … While reading the book, I used the opportunity to revisit several seminal papers and to marvel at the advances they re
ehhh L. Xue Neither a good introduction to Category Theory as a mathematical discipline, nor a particularly thought through work in Philosophy of Mathematics/History of Mathematics. It offers an interesting perspective to contrast against other attempts at writing a history of Category Theory (for example, Leo Corrys), but as far as I see, no one has yet succeeded.The main thesis of this book, as I understand it, is to align Eilenberg and Maclane's work leading up to Category Theory for the Working Mathematician with Klein's Erlangen program. Kl. Accessible, as well as rigorous Situated Agent One of the best introductions to category theory available. Other sources are more concise (e.g., Mclarty, Goldblatt) but, if you would like to approach category and topos theories from a conceptual perspective, Marquis provides an excellent alternative.