Kategorien I Book by Dr. Helmar Schubert - Bookswagon
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Kategorien I

Kategorien I


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About the Book

Dieses Buch entstand aus Aufzeichnungen, die ich fUr die Horer einer Vorlesung im Jahre 1967/68 in Kiel angefertigt hatte. Angesichts der rasch wachsenden Anwendung der kategoriellen Sprache setzt es sich das Ziel, in den zentralen Teil der Theorie einzufUhren und dem weiter Interessierten Zugang zur Literatur zu verschaffen. An Vorkenntnissen sind in der Sache nur die einfachsten Grund begriffe der Mengenlehre und der Algebra erforderlich. Moduln treten zwar von Anfang an in den Beispielen auf, sie werden aber in 15.1 de finiert. Ein Teil der Beispiele entstammt der Topologie. Selbstverstand lich wird das Verstiindnis der Begriffsbildungen wesentlich erleichtert, wenn man mit den Beispielen aus Algebra oder Topologie vertraut ist. 1m Mittelpunkt steht der Begriff des darstellbaren Funktors mit seinen Abwandlungen: Limites und adjungierte Funktorpaare. Es handelt sich urn die Charakterisierung spezieller Objekte durch uni verse lIe Abbildungseigenschaften, die fUr SpezialfiilIe schon lange und im Werk von Bourbaki, bei anderer Sprache, systematisch benutzt wird. Das Yoneda-Lemma wird moglichst friih bereitgestellt. Dagegen wird die Behandlung adjungierter Funktorpaare aufgeschoben, bis sie zu sammenhiingend moglich ist und auch die Kansche Konstruktion so fort angeschlossen werden kann. Filtrierende Coli mites werden gebiih rend beriicksichtigt. Additive Kategorien und Funktorkategorien sind von Anfang an in die Betrachtung einbezogen. Dabei wird die benutzte Mengenlehre dort referiert, wo sich ihr Gebrauch aufdriingt. Nach dem gegenwiirtigen Stand scheinen Universa am handlichsten, und ich ver traue darauf, daB bei einer moglichen Revision der Grundlagen die Substanz der Theorie erhalten bleibt."


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Product Details
  • ISBN-13: 9783540048657
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Height: 203 mm
  • No of Pages: 162
  • Series Title: Heidelberger Taschenbücher
  • Weight: 240 gr
  • ISBN-10: 3540048650
  • Publisher Date: 01 Jan 1970
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Spine Width: 10 mm
  • Width: 133 mm


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