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Philosophy - Epistemology & Philosophy of Science | From a Geometrical Point of View - A Study of the History and Philosophy of Category Theory

From a Geometrical Point of View

A Study of the History and Philosophy of Category Theory

Marquis, Jean-Pierre

2009, X, 310 p.

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  • 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
  • Brings together historical, mathematical and philosophical considerations

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.

Content Level » Research

Keywords » Algebra - Invariant - categorical logic - category theory - geometry - history of mathematics - mathematics - mathematics and foundations - philosophy of mathematics - science

Related subjects » Algebra - Epistemology & Philosophy of Science - Geometry & Topology - History of Mathematical Sciences - Mathematics

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.

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