| Calculus of Fractions and Homotopy Theory Contributor(s): Gabriel, Peter (Author), Zisman, M. (Author) |
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ISBN: 0387037772 ISBN-13: 9780387037776 Publisher: Springer OUR PRICE: $73.10 Product Type: Hardcover - Other Formats Published: January 1967 |
| Additional Information |
| BISAC Categories: - Mathematics | Topology - General - Mathematics | Arithmetic |
| Dewey: 513.83 |
| Physical Information: 168 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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). |