Calculus of Fractions and Homotopy Theory is popular PDF and ePub book, written by Peter Gabriel in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Calculus of Fractions and Homotopy Theory can be Read Online from any device for your convenience.
Calculus of Fractions and Homotopy Theory Book PDF Summary
The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo topic category (IV). This category is, in fact, - according to Chapter VII and a well-known theorem of J. H. C. WHITEHEAD - equivalent to the category of CW-complexes modulo homotopy, i.e. the category whose objects are spaces of the homotopy type of a CW-complex and whose morphisms are homotopy classes of continuous mappings between such spaces. It is also equivalent (I, 1.3) to a category of fractions of the category of topological spaces modulo homotopy, and to the category of Kan complexes modulo homotopy (IV). In order to define our homotopic category, it appears useful to follow as closely as possible methods 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 machinery upon which this work is essentially based includes the usual grounding in category theory - summarized in the Dictionary - and the theory of categories of fractions which forms the subject of the first chapter of the book. The merely topological machinery reduces to a few properties of Kelley spaces (Chapters I and III). The starting point of our study is the category ,10 Iff of simplicial sets (C.S.S. complexes or semi-simplicial sets in a former terminology).
Detail Book of Calculus of Fractions and Homotopy Theory PDF
- Author : Peter Gabriel
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9783642858444
- Genre : Mathematics
- Total Page : 178 pages
- Language : English
- PDF File Size : 14,9 Mb
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