Presentation of homotopy types under a space

الأصل · EN

We compare the structure of a mapping cone in the category Topᵈ of spaces under a space D with differentials in algebraic models like crossed complexes and quadratic complexes. Several subcategories of Topᵈ are identified with algebraic categories. As an application we show that there are exactly 16 essential self--maps of S² x S² fixing the diagonal.