Description

Book Synopsis
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).

Table of Contents
Abstract Homotopy Theory; Case Studies; Exact Sequences; Elementary Homotopy Coherence; Abstract Simple Homotopy Theory; Additive Simple Homotopy Theories.

Abstract Homotopy And Simple Homotopy Theory

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    A Hardback by K Heiner Kamps, Timothy Porter

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      View other formats and editions of Abstract Homotopy And Simple Homotopy Theory by K Heiner Kamps

      Publisher: World Scientific Publishing Co Pte Ltd
      Publication Date: 11/04/1997
      ISBN13: 9789810216023, 978-9810216023
      ISBN10: 9810216025

      Description

      Book Synopsis
      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).

      Table of Contents
      Abstract Homotopy Theory; Case Studies; Exact Sequences; Elementary Homotopy Coherence; Abstract Simple Homotopy Theory; Additive Simple Homotopy Theories.

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