Abstract Homotopy and Simple Homotopy Theory

Couverture
World Scientific, 1997 - 462 pages
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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).
 

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Table des matières

Homotopical algebra
76
Case studies
145
Groupoid enrichment and track homotopy
253
Homotopy coherence
307
Abstract simple homotopy theories
342
Injective simple homotopy theories
402
Glossary of terms from category theory
429
References
447
Index
455
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