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Tool and Object

A History and Philosophy of Category Theory

Ralph Krömer (Autor)

Buch | Hardcover

XXXVI, 367 Seiten

2007 | 2007
Springer Basel (Verlag)
978-3-7643-7523-2 (ISBN)

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Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance.

Prelude: Poincaré, Wittgenstein, Peirce, and the use of concepts.- Category theory in Algebraic Topology.- Category theory in Homological Algebra.- Category theory in Algebraic Geometry.- From tool to object: full-fledged category theory.- Categories as sets: problems and solutions.- Categorial foundations.- Pragmatism and category theory.

From the reviews:

"Krömer provides a more complete historical study of category theory and its applications from the beginnings to about 1970. ... It caught the attention of people interested in conceptual and philosophical issues ... . I recommend Krömer's work highly to anyone who seeks to gain an understanding of category-theoretic mathematics ... . an interesting contribution to the historical philosophy of mathematical practice ... . the book is more successful as a history. It is well produced, and the English is clear enough ... ." (José Ferreirós, Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin, Issue 1, 2010)

Erscheint lt. Verlag	16.2.2007
Reihe/Serie	Science Networks. Historical Studies
Zusatzinfo	XXXVI, 367 p.
Verlagsort	Basel
Sprache	englisch
Maße	170 x 244 mm
Gewicht	763 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
Schlagworte	Algebra • category theory • Epistemology • Grothendieck, Alexander • History of Mathematics • Homological algebra • Kategorientheorie • Mac Lane, Saunders
ISBN-10	3-7643-7523-X / 376437523X
ISBN-13	978-3-7643-7523-2 / 9783764375232
Zustand	Neuware