MARC Record from harvard_bibliographic_metadata

LEADER: 03027nam a2200337Mi 4500
001 010264140-4
005 20140910154323.0
008 070223s2007 sz bm 001 0 eng d
016 7 $a976388979$2GyFmDB
020 $a9783764375232 (hd.bd.)
020 $a376437523X (hd.bd.)
035 0 $aocm85242858
040 $aOHX$cOHX$dBAKER
050 00 $aQA169$b.K76 2007
072 7 $aQA$2lcco
090 $aQA169$b.K76 2007
100 1 $aKrömer, Ralf.
245 10 $aTool and object :$ba history and philosophy of category theory /$cRalf Krömer.
260 $aBasel ;$aBoston :$bBirkhäuser,$cc2007.
300 $axxxvi, 367 p. ;$c24 cm.
440 0 $aScience networks historical studies ;$vv. 32
500 $aDissertation.
504 $aIncludes bibliographical references (p. [321]-341) and indexes.
505 0 $aPrelude: 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.
520 $aThe 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.
650 0 $aCategories (Mathematics)
650 0 $aAlgebra.
650 0 $aMathematics.
650 0 $aMathematics_$xHistory.
988 $a20070322
906 $0OCLC