Generalized Homotopy theory in Categories with a Natural Cone

Details Generalized Homotopy theory in Categories with a Natural Cone Generalized Homotopy theory in Categories with a Natural Cone

2012-03-02

arxiv.org/abs/1203.0424v1

Mathematics

Algebraic Topology

16 pages

Scientific paper

In proper homotopy theory, the original concept of point used in the classical homotopy theory of topological spaces is generalized in order to obtain homotopy groups that study the infinite of the spaces. This idea: "Using any arbitrary object as base point" and even "any morphism as zero morphism" can be developed in most of the algebraic homotopy theories. In particular, categories with a natural cone have a generalized homotopy theory obtained through the relative homotopy relation. Generalized homotopy groups and exact sequences of them are built so that respective classical pointed ones are a particular case of these.

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