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Are you searching for Abstract Homotopy and Simple Homotopy Theory ?
Author : K Heiner Kamps
Publisher : World Scientific Publishing Company
Total Pages : 462
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, Vogts Iemma, Dolds theorem on fibre homotopy equivalences, and homotopy coherence theory). Contents:Abstract Homotopy TheoryHomotopical AlgebraCase StudiesGroupoid Enrichment and Track HomotopyHomotopy CoherenceAbstract Simple Homotopy TheoriesInjective Simple Homotopy Theories Readership: Algebraic topologists , category theorists, both at postgraduate and research level. keywords:Abstract Homotopy Theory;Simple Homotopy Theory;Additive Homotopy Theory;Homotopical Algebra;Homotopy Coherence;Cylinder Functor;Quillen Model Category;Cubical Sets;Simplicial Sets;Groupoids;Simple Homotopy Equivalences;Mapping Cylinder Calculus;Cubical Complex "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." Mathematical Reviews
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