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From a Geometrical Point of View
A Study of the History and Philosophy of Category Theory
Sofort lieferbar | Lieferzeit: Sofort lieferbar I
ISBN-13:
9781402093845
Veröffentl:
2008
Seiten:
310
Autor:
Jean-Pierre Marquis
Serie:
14, Logic, Epistemology, and the Unity of Science
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
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 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.
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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