  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.
