ISBN:
9781402093845
Language:
English
Pages:
Online-Ressource
,
v.: digital
Edition:
Online-Ausg. 2009 Springer eBook Collection. Humanities, Social Science and Law Electronic reproduction; Available via World Wide Web
Series Statement:
Logic, Epistemology, and the Unity of Science 14
Parallel Title:
Print version From a Geometrical Point of View
Keywords:
Algebraic topology
;
Logic, Symbolic and mathematical
;
Science Algebra
;
Mathematics_$xHistory
;
Algebra
;
Philosophy (General)
;
Kategorientheorie
;
Geschichte
Abstract:
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.
Description / Table of Contents:
Introduction; 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.
Note:
Includes bibliographical references and index
,
Electronic reproduction; Available via World Wide Web
DOI:
10.1007/978-1-4020-9384-5
URL:
Volltext
(lizenzpflichtig)
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