From a Geometrical Point of View A Study of the History and Philosophy of Category Theory /

• Main Author: Marquis, Jean-Pierre. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Dordrecht : Springer Netherlands, 2009.
• Series: Logic, Epistemology, and the Unity of Science ; 14
• Subjects: Philosophy (General).; Science > Philosophy.; Algebra.; Mathematics_$xHistory.; Logic, Symbolic and mathematical.; Algebraic topology.; Philosophy.; Philosophy of Science.; Category Theory, Homological Algebra.; Mathematical Logic and Foundations.; History of Mathematics.; Algebraic Topology.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4020-9384-5

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 Kleins Erlangen program in geometry is in fact a particular instance of a general and broad phenomeno...

Table of Contents:

• Introduction
• 1. Category theory and Kleins Erlangen Program
• 2. Introducing categories, functors and natural transformations
• 3. Categories as spaces, functors as transformations
• 4. Discovering fundamental categorical transformations: adjoint functors
• 5. Adjoint functors: what they are, what they mean
• 6. Invariants in foundations: Algebraic logic
• 7. Invariants in foundations: Geometric logic
• Conclusion
• References
• Index.