Category with a natural cone

• Autorzy: Francisco Díaz , Sergio Rodríguez-Machín
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Category; algebraic homotopy theory; cone construction; 55U35; 18C; 55P05; 55P40; 55Q05

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 1
• Strony: 5-33

Daty

wydano

2006-03-01

online

2006-03-01

Twórcy

autor

Francisco Díaz

• Universidad de La Laguna

autor

Sergio Rodríguez-Machín

• Universidad de La Laguna

Bibliografia

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Identyfikatory

DOI

10.1007/s11533-005-0002-5