Abstract Homotopy And Simple Homotopy Theory
Seiten
1997
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-1602-3 (ISBN)
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-1602-3 (ISBN)
Discusses abstract homotopy theory, which is based on the observation that analogues of much of topological homotopy theory and simple homotopy theory exist in many other categories, such as spaces over a fixed base, groupoids, chain complexes and module categories.
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).
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).
Abstract Homotopy Theory; Case Studies; Exact Sequences; Elementary Homotopy Coherence; Abstract Simple Homotopy Theory; Additive Simple Homotopy Theories.
| Erscheint lt. Verlag | 11.4.1997 |
|---|---|
| Verlagsort | Singapore |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 981-02-1602-5 / 9810216025 |
| ISBN-13 | 978-981-02-1602-3 / 9789810216023 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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