From a Geometrical Point of View

A Study of the History and Philosophy of Category Theory

Jean-Pierre Marquis (Autor)

Buch | Softcover

310 Seiten

2010 | Softcover reprint of hardcover 1st ed. 2009
Springer (Verlag)
978-90-481-8117-9 (ISBN)

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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.

Jean-Pierre Marquis teaches logic, epistemology and philosophy of science at the Université de Montréal. He has published papers on category theory, categorical logic, general philosophy of mathematics and philosophy of science.

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.

Erscheint lt. Verlag	28.10.2010
Reihe/Serie	Logic, Epistemology, and the Unity of Science ; 14
Zusatzinfo	X, 310 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
	Naturwissenschaften
ISBN-10	90-481-8117-8 / 9048181178
ISBN-13	978-90-481-8117-9 / 9789048181179
Zustand	Neuware