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Category with a natural cone

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Díaz F., Rodríguez-Machín S.

Open Mathematics

2006

tom 4

nr 1

5-33

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.

Ograniczanie wyników

1 Open Mathematics

1 Díaz F.

1 Rodríguez-Machín S.

1 2006

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Category with a natural cone