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Tool and Object : A History and Philosophy of Category Theory / by Ralph Krömer
(Science Networks. Historical Studies. ISSN:22966080 ; 32)
版 | 1st ed. 2007. |
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出版者 | (Basel : Birkhäuser Basel : Imprint: Birkhäuser) |
出版年 | 2007 |
本文言語 | 英語 |
大きさ | XXXVI, 367 p : online resource |
著者標目 | *Krömer, Ralph author SpringerLink (Online service) |
件 名 | LCSH:Mathematics LCSH:History LCSH:Algebra, Homological FREE:History of Mathematical Sciences FREE:Category Theory, Homological Algebra |
一般注記 | 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 The book is first of all a history of category theory from the beginnings to A. Grothendieck and F.W. Lawvere. Category theory was an important conceptual tool in 20th century mathematics whose influence on some mathematical subdisciplines (above all algebraic topology and algebraic geometry) is analyzed. Category theory also has an important philosophical aspect: on the one hand its set-theoretical foundation is less obvious than for other mathematical theories, and on the other hand it unifies conceptually a large part of modern mathematics and may therefore be considered as somewhat fundamental itself. The role of this philosophical aspect in the historical development is the second focus of the book. Relying on the historical analysis, the author develops a philosophical interpretation of the theory of his own, intending to get closer to how mathematicians conceive the significance of their activity than traditional schools of philosophy of science. The book is the first monography exclusively devoted to the history of category theory. To a substantial extent it considers aspects never studied before. The author uses (and justifies the use of) a methodology combining historical and philosophical approaches. The analysis is not confined to general remarks, but goes into considerable mathematical detail. Hence, the book provides an exceptionally thorough case study compared with other works on history or philosophy of mathematics. The philosophical position developed here (inspired by Peircean pragmatism and Wittgenstein) is an interesting alternative to traditional approaches in philosophy of mathematics like platonism, formalism and intuitionism HTTP:URL=https://doi.org/10.1007/978-3-7643-7524-9 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783764375249 |
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EB00235174 |
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