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Suspension and Loop Objects and Representability of Tracks

Suspension and Loop Objects and Representability of Tracks In the general setting of groupoid enriched categories, notions of suspender and looper of a map are introduced, formalizing a generalization of the classical homotopy-theoretic notions of suspension and loop space. The formalism enables subtle analysis of these constructs. In particular, it is shown that the suspender of a principal coaction splits as a coproduct. This result leads to the notion of theories with suspension and to the cohomological classification of certain groupoid enriched categories. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Suspension and Loop Objects and Representability of Tracks

Baues, H.-J.; Jibladze, M.
Georgian Mathematical Journal , Volume 8 (4) – Dec 1, 2001
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References (15)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2001.683
Publisher site
See Article on Publisher Site

Abstract

In the general setting of groupoid enriched categories, notions of suspender and looper of a map are introduced, formalizing a generalization of the classical homotopy-theoretic notions of suspension and loop space. The formalism enables subtle analysis of these constructs. In particular, it is shown that the suspender of a principal coaction splits as a coproduct. This result leads to the notion of theories with suspension and to the cohomological classification of certain groupoid enriched categories.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Dec 1, 2001

Keywords: Groupoid enriched category; suspension object; loop object; suspender; looper; principal coaction

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