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 eBook
• Language: English
• Published: Dordrecht : Springer Netherlands, 2009.
• Series: Logic, Epistemology, and the Unity of Science ; 14
• Subjects: Philosophy.; Philosophy and science.; Category theory (Mathematics).; Homological algebra.; Mathematics.; History.; Mathematical logic.; Algebraic topology.; Philosophy of Science.; History of Mathematical Sciences.; Category Theory, Homological Algebra.; Mathematical Logic and Foundations.; Algebraic Topology.

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 phenomeno...

Table of Contents:

• Category Theory and Klein’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.