Directed homotopy theory, II. Homotopy constructs.
Grandis, Marco (2002)
Theory and Applications of Categories [electronic only]
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Directed homotopy theory, II. Homotopy constructs.
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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...
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