From a Geometrical Point of View

by Marquis, Jean-pierre

• ISBN13: 9781402093838
• ISBN10: 1402093837
• Format: Hardcover
• Copyright: 2009-02-01
• Publisher: Springer Verlag

Summary

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.

Author Biography

Jean-Pierre Marquis teaches logic, epistemology and philosophy of science at the Universit+¬ de Montr+¬al. He has published papers on category theory, categorical logic, general philosophy of mathematics and philosophy of science.

Table of Contents

Introduction

Category theory and KleinG++s Erlangen Program

Introducing categories, functors and natural transformations

Categories as spaces, functors as transformations

Discovering fundamental categorical transformations: adjoint functors

Adjoint functors: what they are, what they mean

Invariants in foundations: Algebraic logic

Invariants in foundations: Geometric logic

Conclusion

References

Index

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