Calculus of Fractions and Homotopy Theory by Peter Gabriel

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  • Title: Calculus of Fractions and Homotopy Theory
  • Author: Peter Gabriel
  • Category: Mathematics
  • Date: December 2012
  • Lenguage: English
  • Pages: unknown
  • ISBN: 3642858449

 

Ebook description:

The predominant function of the current work is to current to the reader a very good category for the examine of homotopy, specifically the homo¬≠ matter category (IV). This category is, in truth, – in response to Chapter VII and a well known theorem of J. H. C. WHITEHEAD – equal to the category of CW-complexes modulo homotopy, i.e. the category whose objects are areas of the homotopy kind of a CW-complex and whose morphisms are homotopy courses of steady mappings between such areas. It can also be equal (I, 1.3) to a category of fractions of the category of topological areas modulo homotopy, and to the category of Kan complexes modulo homotopy (IV). In order to outline our homotopic category, it seems helpful to comply with as carefully as attainable strategies which have proved efficacious in homo¬≠ logical algebra. Our category is thus the” topological” analogue of the derived category of an abelian category (VERDIER). The algebraic equipment upon which this work is actually based mostly contains the standard grounding in category principle – summarized within the Dictionary – and the idea of classes of fractions which types the topic of the primary chapter of the e-book. The merely topological equipment reduces to some properties of Kelley areas (Chapters I and III). The place to begin of our examine is the category ,10 Iff of simplicial units (C.S.S. complexes or semi-simplicial units in a former terminology)

 

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