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ABSTRACT HOMOTOPY AND SIMPLE HOMOTOPY THEORY

by K H Kamps (Fern Universität, Hagen, Germany) & T Porter (University of Wales, Bangor, UK)

The abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many other categories (e.g. spaces over a fixed base, groupoids, chain complexes, module categories). Studying categorical versions of homotopy structure, such as cylinders and path space constructions, enables not only a unified development of many examples of known homotopy theories but also reveals the inner working of the classical spatial theory. This demonstrates the logical interdependence of properties (in particular the existence of certain Kan fillers in associated cubical sets) and results (Puppe sequences, Vogt's Iemma, Dold's theorem on fibre homotopy equivalences, and homotopy coherence theory).

Publishes by: World Scientific


Contents:

  • Abstract Homotopy Theory
  • Homotopical Algebra
  • Case Studies
  • Groupoid Enrichment and Track Homotopy
  • Homotopy Coherence
  • Abstract Simple Homotopy Theories
  • Injective Simple Homotopy Theories


Readership: Algebraic topologists, category theorists, both at postgraduate and research level.


"This book provides a thorough and well-written guide to abstract homotopy theory. It could well serve as a graduate text in this topic, or could be studied independently by someone with a background in basic algebra, topology, and category theory."


Latest version of this page: 21/12/99

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Mathematical Reviews