rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Tool and Object
    sub title: A History and Philosophy of Category Theory
  name:
    name part: Krömer, Ralf.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2007
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXXVI, 367 p. online resource.
  abstract: 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.
  table of contents: 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.
  note: by Ralf Krömer.
  subject:
    topic: Mathematics
  subject:
    topic: Category theory (Mathematics)
  subject:
    topic: Homological algebra
  subject:
    topic: History
  subject:
    topic: Mathematics
  subject:
    topic: History of Mathematical Sciences
  subject:
    topic: Category Theory, Homological Algebra
  classification: QA21-27
  classification: 510.9
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Science Networks. Historical Studies ; 32
  identifier: 9783764375249
  identifier: http://dx.doi.org/10.1007/978-3-7643-7524-9
  record info:
    record creation date: 100301
    record change date: 20151204183523.0
    record identifier: 978-3-7643-7524-9