Abstract Homotopy And Simple Homotopy Theory
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A01=K Heiner Kamps
A01=Timothy Porter
Abstract Homotopy Theory
Additive Homotopy Theory
Author_K Heiner Kamps
Author_Timothy Porter
Category=PBM
Category=PBP
Cubical Complex
Cubical Sets
Cylinder Functor
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Groupoids
Homotopical Algebra
Homotopy Coherence
Mapping Cylinder Calculus
Quillen Model Category
Simple Homotopy Equivalences
Simple Homotopy Theory
Simplicial Sets
Product details
- ISBN 9789810216023
- Publication Date: 11 Apr 1997
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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).
