Category with a natural cone
Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based ob...
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Published in | Open mathematics (Warsaw, Poland) Vol. 4; no. 1; pp. 5 - 33 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Warsaw
Versita
01.03.2006
De Gruyter Poland De Gruyter |
Subjects | |
Online Access | Get full text |
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Summary: | Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given. We point out that the main results of this paper were already stated in [3], and the purpose of this article is to give full details of the foregoing. |
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ISSN: | 2391-5455 2391-5455 |
DOI: | 10.1007/s11533-005-0002-5 |